Calcium-Containing High-Index Phosphate Glasses

ABSTRACT

Glass compositions include phosphorus oxide (P 2 O 5 ), niobia (Nb 2 O 5 ), titania (TiO 2 ), potassium oxide (K 2 O) and calcium oxide (CaO) as essential components and may optionally include barium oxide (BaO), sodium oxide (Na 2 O), lithium oxide (Li 2 O), tungsten oxide (WO 3 ), bismuth oxide (Bi 2 O 3 ), tantalum oxide (Ta 2 O 5 ), silica (SiO 2 ) and other components. The glasses may be characterized by high refractive index at 587.56 nm at comparably low density at room temperature.

This application claims the benefit of priority under 35 U.S.C. § 119 ofU.S. Provisional Application Ser. No. 63/140,414 filed on Jan. 22, 2021,the content of which is relied upon and incorporated herein by referencein its entirety.

FIELD

The present disclosure generally relates to phosphate glasses having ahigh refractive index and low density. Also, it relates to glasses withhigh optical dispersion.

BACKGROUND

Glass is used in a variety of optical devices, examples of which includeaugmented reality devices, virtual reality devices, mixed realitydevices, eye wear, etc. Desirable properties for this type of glassoften include a high refractive index and a low density. Additionaldesirable properties may include high transmission in the visible andnear-ultraviolet (near-UV) range of the electromagnetic spectrum and/orlow optical dispersion. It can be challenging to find glasses having thedesired combination of these properties and which can be formed fromcompositions having good glass-forming ability. For example, generallyspeaking, as the refractive index of a glass increases, the density alsotends to increase. Species such as TiO₂ and Nb₂O₅ are often added toincrease the refractive index of a glass without increasing the densityof the glass. However, these materials often absorb blue and UV light,which can undesirably decrease the transmittance of light in this regionof the spectrum by the glass. Often, attempts to increase the refractiveindex of a glass while maintaining a low density, and without decreasingtransmittance in the blue and UV region of the spectrum, can result in adecrease in the glass-forming ability of the material. For example,crystallization and/or liquid-liquid phase separation can occur duringcooling of the glass melt at cooling rates that are generally acceptablein the industry. Typically, the decrease in glass-forming abilityappears as the amount of certain species, such as ZrO₂, Y₂O₃, Sc₂O₃,BeO, etc. increases.

Low density, high refractive index glasses often belong to one of twotypes of chemical systems, based on the glass formers used: (a)silicoborate or borosilicate glasses in which SiO₂ and/or B₂O₃ are usedas the main glass formers and (b) phosphate glasses in which P₂O₅ isused as a main glass former. Glasses which rely on other oxides as mainglass formers, such as GeO₂, TeO₂, Bi₂O₃, and V₂O₅, can be challengingto use due to cost, glass-forming ability, optical properties, and/orproduction requirements.

Phosphate glasses can be characterized by a high refractive index andlow density, however, phosphate glasses can be challenging to producedue to volatilization of P₂O₅ from the melts and/or risks of platinumincompatibility. In addition, phosphate glasses are often highly coloredand may require an extra bleaching step to provide a glass having thedesired transmittance characteristic. Furthermore, phosphate glassesexhibiting a high refractive index also tend to have an increase inoptical dispersion, which may be usable for some applications.

In view of these considerations, there is a need for phosphate glasseshaving a high refractive index and low density, optionally incombination with a high transmittance in the visible and near UV-range,and/or which are made from compositions that provide good glass-formingability.

SUMMARY

According to an embodiment of the present disclosure, a glass comprisinga plurality of components is disclosed, the glass has a composition ofthe components comprising greater than or equal to 10.0 mol. % and lessthan or equal to 40.0 mol. % P₂O₅, greater than or equal to 0.5 mol. %and less than or equal to 50.0 mol. % TiO₂, greater than or equal to 0.5mol. % and less than or equal to 35.0 mol. % K₂O, greater than or equalto 0.5 mol. % and less than or equal to 35.0 mol. % CaO, greater than orequal to 0.0 mol. % and less than or equal to 50.0 mol. % Nb₂O₅, greaterthan or equal to 0.0 mol. % and less than or equal to 15.0 mol. % MgO,greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol.% Al₂O₃, greater than or equal to 0.0 mol. % and less than or equal to4.5 mol. % Li₂O, greater than or equal to 0.0 mol. % and less than orequal to 1.0 mol. % V₂O₅, greater than or equal to 4.0 mol. % RO,greater than or equal to 0.0 mol. % and less than or equal to 20.0 mol.% for a sum of TeO₂+SnO₂+SnO, greater than or equal to 0.0 mol. % andless than or equal to 15.0 mol. % for a sum of SiO₂+GeO₂ and mayoptionally contain one or more components selected from Na₂O, WO₃,Bi₂O₃, B₂O₃, BaO, SrO, ZnO, PbO, ZrO₂, Tl₂O, Ag₂O, Cs₂O, Ga₂O₃, La₂O₃,MoO₃ and Ta₂O₅, the glass satisfying the condition:P_(n)−(1.54+0.1*P_(d))>0.00, where P_(n) is a refractive index parametercalculated from the glass composition in terms of mol. % of thecomponents according to the Formula (I):

P_(n)=−0.0043794*P₂O₅+0.0072428*Nb₂O₅+0.0037304*TiO₂−0.00039553*BaO−0.0032012*K₂O−0.00060689*CaO−0.0024218*Na₂O−0.0014988*Li₂O+0.0028587*WO₃+0.0083295*Bi₂O₃−0.0031637*B₂O₃−0.0030702*SiO₂−0.00030248*ZnO+0.0020025*ZrO₂−0.0018173*MgO−0.0032886*Al₂O₃+0.0024221*TeO₂+0.0038137*PbO−0.0016392*GeO₂+0.0063024*Tl₂O+0.0048765*Ag₂O+1.81451,  (I)

P_(d) is a density parameter, calculated from the glass composition interms of mol. % of the components according to the Formula (II):

P_(d)[g/cm³]=3.98457−0.015773*Al₂O₃−0.014501*B₂O₃+0.019328*BaO+0.060758*Bi₂O₃−0.0012685*CaO+0.023111*CdO+0.0053184*Cs₂O+0.011488*Ga₂O₃−0.0015416*GeO₂−0.013342*K₂O+0.058319*La₂O₃−0.007918*Li₂O−0.0021423*MgO−0.0024413*MoO₃−0.0082226*Na₂O+0.0084961*Nb₂O₅−0.020501*P₂O₅+0.038898*PbO−0.012720*SiO₂+0.013948*SrO+0.047924*Ta₂O₅+0.011248*TeO₂−0.0092491*V₂O₅+0.028913*WO₃+0.0074702*ZnO+0.0096721*ZrO₂,  (II)

where RO is a total sum of divalent metal oxides and a symbol “*” meansmultiplication.

According to another embodiment of the present disclosure, a glasscomprising a plurality of components is disclosed, the glass has acomposition of the components comprising greater than or equal to 10.0mol. % and less than or equal to 40.0 mol. % P₂O₅, greater than or equalto 1.0 mol. % and less than or equal to 50.0 mol. % TiO₂, greater thanor equal to 1.0 mol. % and less than or equal to 35.0 mol. % K₂O,greater than or equal to 1.0 mol. % and less than or equal to 35.0 mol.% CaO, greater than or equal to 0.0 mol. % and less than or equal to50.0 mol. % Nb₂O₅, greater than or equal to 0.0 mol. % and less than orequal to 15.0 mol. % MgO, greater than or equal to 0.0 mol. % and lessthan or equal to 10.0 mol. % Al₂O₃, greater than or equal to 0.0 mol. %and less than or equal to 1.0 mol. % V₂O₅, greater than or equal to 4.0mol. % RO, greater than or equal to 0.0 mol. % and less than or equal to20.0 mol. % for a sum of TeO₂+SnO₂+SnO, greater than or equal to 0.0mol. % and less than or equal to 15.0 mol. % for a sum of SiO₂+GeO₂ andmay optionally contain one or more components selected from Na₂O, Li₂O,WO₃, Bi₂O₃, B₂O₃, BaO, SrO, ZnO, PbO, ZrO₂, Tl₂O, Ag₂O, Ga₂O₃, MoO₃ andTa₂O₅, the glass satisfying the conditions: P_(n)>1.75 andP_(ν)−(64.5-23.4*P_(n))<0.00, where P_(n) is a refractive indexparameter calculated from the glass composition in terms of mol. % ofthe components according to the Formula (I):

P_(n)=−0.0043794*P₂O₅+0.0072428*Nb₂O₅+0.0037304*TiO₂−0.00039553*BaO−0.0032012*K₂O−0.00060689*CaO−0.0024218*Na₂O−0.0014988*Li₂O+0.0028587*WO₃+0.0083295*Bi₂O₃−0.0031637*B₂O₃−0.0030702*SiO₂−0.00030248*ZnO+0.0020025*ZrO₂−0.0018173*MgO−0.0032886*Al₂O₃+0.0024221*TeO₂+0.0038137*PbO−0.0016392*GeO₂+0.0063024*Tl₂O+0.0048765*Ag₂O+1.81451,  (I)

P_(ν) is a dispersion parameter, calculated from the glass compositionin terms of mol. % of the components according to the Formula (III):

P_(ν)=exp(2.11+0.0438*(exp(3.25980+0.0072248*Al₂O₃+0.0055494*B₂O₃+0.0024164*BaO−0.00849*Bi₂O₃+0.0029812*CaO+0.0092768*CdO+0.0099821*Ga₂O₃−0.0038579*GeO₂+0.0028062*K₂O+0.0031951*Li₂O+0.0027011*MgO+0.007976*MoO₃+0.0028705*Na₂O−0.013374*Nb₂O₅+0.0072007*P₂O₅−0.0049796*PbO+0.0032241*SiO₂+0.0050024*SrO−0.002136*Ta₂O₅−0.0032329*TeO₂−0.009788*TiO₂+0.0074782*V₂O₅−0.0057095*WO₃+0.0032826*ZnO+0.009302*ZrO₂))),  (III)

where RO is a total sum of divalent metal oxides and a symbol “*” meansmultiplication.

These and other aspects, objects, and features of the present disclosurewill be understood and appreciated by those skilled in the art uponstudying the following specification, claims, and appended drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plot illustrating the relationship between the refractiveindex n_(d) and the refractive index parameter P_(n) calculated byformula (I) for some Comparative Glasses and some Exemplary Glassesaccording to an embodiment of the present disclosure.

FIG. 2 is a plot illustrating the relationship between the density atroom temperature d_(RT) and the density parameter P_(d) calculated byformula (II) for some Comparative Glasses and some Exemplary Glassesaccording to an embodiment of the present disclosure.

FIG. 3 is a plot illustrating the relationship between the Abbe numberν_(d) and the dispersion parameter P_(ν) calculated by formula (III) forsome Comparative Glasses and some Exemplary Glasses according to anembodiment of the present disclosure.

FIG. 4 is a plot illustrating the relationship between the refraction(n_(d)−1)/d_(RT) and the parameter P_(ref) calculated by formula (IV)for some Comparative Glasses and some Exemplary Glasses according to anembodiment of the present disclosure.

FIG. 5 is a plot of an exemplary cooling schedule according to a “15 mintest” condition and a “2.5 min test” condition for some ExemplaryGlasses according to an embodiment of the present disclosure.

FIG. 6 is a plot illustrating the relationship between the densityparameter P_(d) and the refractive index parameter P_(n) for someComparative Glasses and some Exemplary Glasses according to anembodiment of the present disclosure.

FIG. 7 is a plot illustrating the relationship between the density atroom temperature d_(RT) and the refractive index n_(d) for someComparative Glasses and some Exemplary Glasses according to anembodiment of the present disclosure.

FIG. 8 is a plot illustrating the relationship between P_(n) and P_(ν)for some Comparative Glasses and some Exemplary Glasses according to anembodiment of the present disclosure.

FIG. 9 is a plot illustrating the relationship between the refractiveindex n_(d) and the Abbe number ν_(d) for some Comparative Glasses andsome Exemplary Glasses according to an embodiment of the presentdisclosure.

DETAILED DESCRIPTION

In the following detailed description, for purposes of explanation andnot limitation, example embodiments disclosing specific details are setforth to provide a thorough understanding of various principles of thepresent disclosure. However, it will be apparent to one having ordinaryskill in the art, having had the benefit of the present disclosure, thatthe present disclosure may be practiced in other embodiments that departfrom the specific details disclosed herein. Moreover, descriptions ofwell-known devices, methods and materials may be omitted so as not toobscure the description of various principles of the present disclosure.Finally, wherever applicable, like reference numerals refer to likeelements.

Unless otherwise expressly stated, it is in no way intended that anymethod set forth herein be construed as requiring that its steps beperformed in a specific order. Accordingly, where a method claim doesnot actually recite an order to be followed by its steps, or it is nototherwise specifically stated in the claims or descriptions that thesteps are to be limited to a specific order, it is in no way intendedthat an order be inferred, in any respect. This holds for any possiblenon-express basis for interpretation, including, without limitation,matters of logic with respect to arrangement of steps or operationalflow; plain meaning derived from grammatical organization orpunctuation; the number or type of embodiments described in thespecification.

As used herein, the term “and/or,” when used in a list of two or moreitems, means that any one of the listed items can be employed by itself,or any combination of two or more of the listed items can be employed.For example, if a composition is described as containing components A,B, and/or C, the composition can contain A alone; B alone; C alone; Aand B in combination; A and C in combination; B and C in combination; orA, B, and C in combination.

Modifications of the disclosure will occur to those skilled in the artand to those who make or use the disclosure. Therefore, it is understoodthat the embodiments shown in the drawings and described above aremerely for illustrative purposes and not intended to limit the scope ofthe disclosure, which is defined by the following claims, as interpretedaccording to the principles of patent law, including the doctrine ofequivalents.

As used herein, the term “about” means that amounts, sizes,formulations, parameters, and other quantities and characteristics arenot and need not be exact, but may be approximate and/or larger orsmaller, as desired, reflecting tolerances, conversion factors, roundingoff, measurement error and the like, and other factors known to thoseskilled in the art. When the term “about” is used in describing a valueor an end-point of a range, the disclosure should be understood toinclude the specific value or end-point referred to. Whether or not anumerical value or end-point of a range in the specification recites“about,” the numerical value or end-point of a range is intended toinclude two embodiments: one modified by “about,” and one not modifiedby “about.” It will be further understood that the end-points of each ofthe ranges are significant both in relation to the other end-point, andindependently of the other end-point.

The term “formed from” can mean one or more of comprises, consistsessentially of, or consists of. For example, a component that is formedfrom a particular material can comprise the particular material, consistessentially of the particular material, or consist of the particularmaterial.

The terms “free” and “substantially free” are used interchangeablyherein to refer to an amount and/or an absence of a particular componentin a glass composition that is not intentionally added to the glasscomposition. It is understood that the glass composition may containtraces of a particular constituent component as a contaminant or a trampin an amount of less than 0.10 mol %.

As used herein, the term “tramp”, when used to describe a particularconstituent component in a glass composition, refers to a constituentcomponent that is not intentionally added to the glass composition andis present in an amount of less than 0.05 mol %. Tramp components may beunintentionally added to the glass composition as an impurity in anotherconstituent component and/or through migration of the tramp componentinto the composition during processing of the glass composition.

The term “glass former” is used herein to refer to a component that,being solely present in the glass composition (i.e., without othercomponents, except for tramps), is able to form a glass when cooling themelt at a rate of not greater than about 200° C./min to about 300°C./min.

The term “modifier”, as used herein, refers to the oxides of monovalentor divalent metals, i.e., R₂O or RO, where “R” stands for a cation.Modifiers can be added to a glass composition to change the atomicstructure of the melt and the resulting glass. In some embodiments, themodifier may change the coordination numbers of cations present in theglass formers (e.g., boron in B₂O₃), which may result in forming a morepolymerized atomic network and, as a result, may provide better glassformation.

As used herein, the term “RO” refers to a total content of divalentmetal oxides, the term “R₂O” refers to a total content of monovalentmetal oxides, and the term “Alk₂O” refers to a total content of alkalimetal oxides. The term R₂O encompasses alkali metal oxides (Alk₂O), inaddition to other monovalent metal oxides, such as Ag₂O, Tl₂O, and Hg₂O,for example. As discussed below, in the present disclosure, a rare earthmetal oxide is referred to herein by its normalized formula (RE₂O₃) inwhich the rare earth metal has the redox state “+3,” and thus rare earthmetal oxides are not encompassed by the term RO.

As used herein, the term “rare earth metals” refers to the metals listedin the Lanthanide Series of the IUPAC Periodic Table, plus yttrium andscandium. As used herein, the term “rare earth metal oxides,” is used torefer to the oxides of rare earth metals in different redox states, suchas “+3” for lanthanum in La₂O₃, “+4” for cerium in CeO₂, “+2” foreuropium in EuO, etc. In general, the redox states of rare earth metalsin oxide glasses may vary and, in particular, the redox state may changeduring melting, based on the batch composition and/or the redoxconditions in the furnace where the glass is melted and/or heat-treated(e.g., annealed). Unless otherwise specified, a rare earth metal oxideis referred to herein by its normalized formula in which the rare earthmetal has the redox state “+3.” Accordingly, in the case in which a rareearth metal having a redox state other than “+3” is added to the glasscomposition batch, the glass compositions are recalculated by adding orremoving some oxygen to maintain the stoichiometry. For example, whenCeO₂ (with cerium in redox state “+4”) is used as a batch component, theresulting glass composition is recalculated assuming that two moles ofCeO₂ is equivalent to one mole of Ce₂O₃, and the resulting glasscomposition is presented in terms of Ce₂O₃. As used herein, the term“RE_(m)O_(n)” is used to refer to the total content of rare earth metaloxides in all redox states present, and the term “RE₂O₃” is used torefer to the total content of rare earth metal oxides in the “+3” redoxstate.

The measured density values for the glasses reported herein weremeasured at room temperature in units of g/cm³ by Archimedes method inwater with an error of 0.001 g/cm³. As used herein, density measurementsat room temperature (specified as d_(RT) and expressed herein in unitsof g/cm³) are indicated as being measured at 20° C. or 25° C., andencompass measurements obtained at temperatures that may range from 20°C. to 25° C. It is understood that room temperature may vary betweenabout 20° C. to about 25° C., however, for the purposes of the presentdisclosure, the variation in density within the temperature range of 20°C. to 25° C. is expected to be less than the error of 0.001 g/cm³, andthus is not expected to impact the room temperature density measurementsreported herein.

As used herein, the term “refraction” refers to the relationship of therefractive index to the density according to the ratio:(n_(d)−1)/d_(RT), where the refractive index n_(d) is measured at 587.56nm and the density d_(RT) is measured in g/cm³ at 25° C. The ratio(n_(d)−1)/d_(RT), or refraction, may characterize the relationshipbetween the refractive index n_(d) and the density d_(RT). The higherthe refraction value, the higher the refractive index is at a givendensity.

As used herein, good glass-forming ability refers to a resistance of themelt to devitrification as the material cools. Glass-forming ability canbe measured by determining the critical cooling rate of the melt. Theterms “critical cooling rate” or “v_(cr)” are used herein to refer tothe minimum cooling rate at which a melt of a given composition forms aglass free of crystals visible under an optical microscope undermagnification from 100× to 500×. The critical cooling rate can be usedto measure the glass-forming ability of a composition, i.e., the abilityof the melt of a given glass composition to form glass when cooling.Generally speaking, the lower the critical cooling rate, the better theglass-forming ability.

The term “liquidus temperature” (denoted “T_(liq)”) is used herein torefer to a temperature above which the glass composition is completelyliquid with no crystallization of constituent components of the glass.The liquidus temperature values reported herein were obtained bymeasuring samples using one of the following three tests: (1) DSC(differential scanning calorimetry), (2) isothermal hold of sampleswrapped in platinum foil, or (3) gradient boat liquidus method. Thetests were crosschecked and similar results were obtained for each ofthe tests. For samples measured using DSC, powdered samples were heatedat 10 K/min to 1250° C. The end of the endothermal event correspondingto the melting of crystals was taken as the liquidus temperature. Forsamples measured using the isothermal hold method, a glass block (about1 cm³) was wrapped in platinum foil, to avoid volatilization, placed ina furnace at a given temperature for 17 hours, then quickly removed fromthe furnace and cooled in air. The glass block was then observed underan optical microscope to check for crystals in the bulk of the sample.Sparse surface crystals were ignored if they appeared after holding atthe temperature that did not exceed the observed liquidus temperature asdescribed above for more than 30-40° C.; otherwise, the test wasrepeated. For samples measured using the gradient boat liquidus method,the procedure described in the standard ASTM C829-81 was followed. Thisinvolves placing crushed glass particles in a platinum boat, placing theboat in a furnace having a region of gradient temperatures, heating theboat in an appropriate temperature region for 24 hours, and determiningby means of microscopic examination the highest temperature at whichcrystals appear in the interior of the glass. More particularly, theglass sample is removed from the Pt boat in one piece, and examinedusing polarized light microscopy to identify the location and nature ofcrystals which have formed against the Pt and air interfaces, and in theinterior of the sample. Because the gradient of the furnace is very wellknown, temperature vs. location can be well estimated, within 5-10° C.The temperature at which crystals are observed in the internal portionof the sample is taken to represent the liquidus of the glass (for thecorresponding test period). Testing is sometimes carried out at longertimes (e.g. 72 hours), to observe slower growing phases. The liquidusviscosity in poises was determined from the liquidus temperature and thecoefficients of the Fulcher equation.

The refractive index values reported herein were measured at roomtemperature (about 25° C.), unless otherwise specified. The refractiveindex values for a glass sample were measured using a Metricon Model2010 prism coupler refractometer with an error of about ±0.0002. Usingthe Metricon, the refractive index of a glass sample was measured at twoor more wavelengths of about 406 nm, 473 nm, 532 nm, 633 nm, 828 nm, and1064 nm. The measured dependence characterizes the dispersion and wasthen fitted with a Cauchy's law equation or Sellmeier equation to allowfor calculation of the refractive index of the sample at a givenwavelength of interest between the measured wavelengths. The term“refractive index n_(d)” is used herein to refer to a refractive indexcalculated as described above at a wavelength of 587.56 nm, whichcorresponds to the helium d-line wavelength. The term “refractive indexn_(c)” is used herein to refer to a refractive index calculated asdescribed above at a wavelength of 656.3 nm. The term “refractive indexn_(F)” is used herein to refer to a refractive index calculated asdescribed above at a wavelength of 486.1 nm. The term “refractive indexn_(g)” is used herein to refer to a refractive index calculated asdescribed above at a wavelength of 435.8 nm.

As used herein, the terms “high refractive index” or “high index” refersto a refractive index value n_(d) of a glass that is greater than orequal to at least 1.80, unless otherwise indicated. Where indicated, theterms “high refractive index” or “high index” refer to a refractiveindex value of a glass that is greater than or equal to at least 1.85,or greater than or equal to 1.90, or greater than or equal to 1.95, orgreater than or equal to 2.00.

The terms “dispersion” and “optical dispersion” are used interchangeablyto refer to a difference or ratio of the refractive indices of a glasssample at predetermined wavelengths. One numerical measure of opticaldispersion reported herein is the Abbe number, which can be calculatedby the formula: ν_(x)=(n_(x)−1)/(n_(F)−n_(c)), where “x” in the presentdisclosure stands for one of the commonly used wavelengths (for example,587.56 nm [d-line] for v_(d) or 589.3 nm [D-line] for V_(D)), n_(x) isthe refractive index at this wavelength (for example, n_(d) for ν_(d)and n_(D) for ν_(D)), and n_(F) and n_(c) are refractive indices at thewavelengths 486.1 nm (F-line) and 656.3 nm (C-line), respectively. Thenumerical values of ν_(d) and ν_(D) differ very slightly, mostly within±0.1% to ±0.2%. As reported herein, the dispersion of a glass sample isrepresented by the Abbe number (ν_(d)), which characterizes therelationship between the refractive indices of the sample at threedifferent wavelengths according to the following formula:ν_(d)=(n_(d)−1)/(n_(F)−n_(c)), where n_(d) is the calculated refractiveindex at 587.56 nm (d-line), n_(F) is the calculated refractive index at486.1 nm (F-line), and n_(c) is the calculated refractive index at 656.3nm (C-line). A higher Abbe number corresponds to a lower opticaldispersion.

The numerical value for an Abbe number corresponding to “highdispersion” or “low dispersion” may vary depending on the refractiveindices for which the Abbe number is calculated. In some cases, an Abbenumber corresponding to “low dispersion” for a high refractive indexglass may be lower than an Abbe number corresponding to “low dispersion”for a low refractive index glass. In other words, as the calculatedrefractive index value increases, the value of the Abbe numbercorresponding to low dispersion decreases. The same relates to “highdispersion” as well.

The term “α,” or “α₂₀₋₃₀₀,” as used herein, refers to the coefficient oflinear thermal expansion (CTE) of the glass composition over atemperature range from 20° C. (room temperature, or RT) to 300° C. Thisproperty is measured by using a horizontal dilatometer (push-roddilatometer) in accordance with ASTM E228-11. The numeric measure of ais linear average value in a specified temperature range (e.g., RT to300° C.) expressed as α=ΔL/(L₀ΔT), where L₀ is the linear size of asample at some temperature within or near the measured range, and L isthe change in the linear size (ΔL) in the measured temperature range ΔT.

The Young's elastic modulus E and the Poisson's ratio μ are measured byusing Resonant Ultrasound Spectroscopy, using a Quasar RUSpec 4000available from ITW Indiana Private Limited, Magnaflux Division.

The glass transition temperature (T_(g)) is measured by differentialscanning calorimeter (DSC) at the heating rate of 10 K/min after coolingin air.

The term “annealing point,” as used herein, refers to the temperaturedetermined according to ASTM C598-93(2013), at which the viscosity of aglass of a given glass composition is approximately 10^(13.2) poise.

The symbol “*” means multiplication when used in any formula herein.

Glass composition may include phosphorus oxide (P₂O₅). The glasscompositions in the embodiments described herein comprise phosphorusoxide (P₂O₅) as a main glass former. Greater amounts of P₂O₅ increasethe melt viscosity at a given temperature, which inhibitscrystallization from the melt when cooling and, therefore, improves theglass-forming ability of the melt (i.e. lowers the critical cooling rateof the melt). However, P₂O₅, being added to a glass composition,significantly decreases the refractive index, which makes it moredifficult to reach high index. Accordingly, the content of P₂O₅ inhigh-index glasses is limited. In embodiments, the glass may containphosphorus oxide (P₂O₅) in an amount from greater than or equal to 10.0mol. % to less than or equal to 40.0 mol. % and all ranges andsub-ranges between the foregoing values. In some embodiments, the glasscomposition may contain P₂O₅ in an amount greater than or equal to 10.0mol. %, greater than or equal to 11.0 mol. %, greater than or equal to12.0 mol. %, greater than or equal to 13.0 mol. %, greater than or equalto 15.0 mol. %, greater than or equal to 20.0 mol. %, greater than orequal to 21.0 mol. %, greater than or equal to 21.7 mol. %, greater thanor equal to 22.0 mol. %, greater than or equal to 23.9 mol. %, greaterthan or equal to 25.0 mol. %, greater than or equal to 30.0 mol. %,greater than or equal to 35.0 mol. %, greater than or equal to 37.0 mol.%, greater than or equal to 38.0 mol. %, or greater than or equal to39.0 mol. %. In some other embodiments, the glass composition maycontain P₂O₅ in an amount less than or equal to 40.0 mol. %, less thanor equal to 39.0 mol. %, less than or equal to 38.0 mol. %, less than orequal to 37.0 mol. %, less than or equal to 35.0 mol. %, less than orequal to 30.0 mol. %, less than or equal to 29.0 mol. %, less than orequal to 25.0 mol. %, less than or equal to 24.7 mol. %, less than orequal to 20.0 mol. %, less than or equal to 15.0 mol. %, less than orequal to 13.0 mol. %, less than or equal to 12.0 mol. %, or less than orequal to 11.0 mol. %. In some more embodiments, the glass compositionmay contain P₂O₅ in an amount greater than or equal to 10.0 mol. % andless than or equal to 40.0 mol. %, greater than or equal to 15.0 mol. %and less than or equal to 35.0 mol. %, greater than or equal to 21.0mol. % and less than or equal to 30.0 mol. %, greater than or equal to21.7 mol. % and less than or equal to 24.7 mol. %, greater than or equalto 22.0 mol. % and less than or equal to 29.0 mol. %, greater than orequal to 23.91 mol. % and less than or equal to 25.0 mol. %, greaterthan or equal to 10.0 mol. % and less than or equal to 35.0 mol. %,greater than or equal to 11.0 mol. % and less than or equal to 24.7 mol.%, greater than or equal to 11.0 mol. % and less than or equal to 12.0mol. %, greater than or equal to 12.0 mol. % and less than or equal to24.7 mol. %, greater than or equal to 13.0 mol. % and less than or equalto 37.0 mol. %, greater than or equal to 13.0 mol. % and less than orequal to 29.0 mol. %, greater than or equal to 13.0 mol. % and less thanor equal to 20.0 mol. %, greater than or equal to 15.0 mol. % and lessthan or equal to 37.0 mol. %, greater than or equal to 15.0 mol. % andless than or equal to 29.0 mol. %, greater than or equal to 20.0 mol. %and less than or equal to 29.0 mol. %, greater than or equal to 24.7mol. % and less than or equal to 40.0 mol. %, greater than or equal to24.7 mol. % and less than or equal to 29.0 mol. %, greater than or equalto 25.0 mol. % and less than or equal to 40.0 mol. %, greater than orequal to 25.0 mol. % and less than or equal to 38.0 mol. %, greater thanor equal to 25.0 mol. % and less than or equal to 35.0 mol. %, greaterthan or equal to 29.0 mol. % and less than or equal to 38.0 mol. %,greater than or equal to 25.0 mol. % and less than or equal to 36.0 mol.%, greater than or equal to 13.0 mol. % and less than or equal to 26.0mol. %, or greater than or equal to 14.0 mol. % and less than or equalto 30.0 mol. %.

Glass composition may include silica (SiO₂). Silica may play a role ofan additional glass-former. Silica, as well as P₂O₅, may help toincrease the liquidus viscosity and, therefore, protect a glasscomposition from crystallization. However, adding SiO₂ to a glasscomposition may cause liquid-liquid phase separation, which may causedevitrification and/or reducing the transmittance of the resultingglass. Also, SiO₂ is a low refractive index component and makes itdifficult to achieve high index glasses. Accordingly, the content ofSiO₂ in the embodiments of the present disclosure is limited, or glassesmay be substantially free of SiO₂. In embodiments, the glass may containsilica (SiO₂) in an amount from greater than or equal to 0.0 mol. % toless than or equal to 15.0 mol. % and all ranges and sub-ranges betweenthe foregoing values. In some embodiments, the glass composition maycontain SiO₂ in an amount greater than or equal to 0.0 mol. %, greaterthan or equal to 1.0 mol. %, greater than or equal to 2.0 mol. %,greater than or equal to 3.0 mol. %, greater than or equal to 5.0 mol.%, greater than or equal to 10.0 mol. %, greater than or equal to 12.0mol. %, greater than or equal to 13.0 mol. %, or greater than or equalto 14.0 mol. %. In some other embodiments, the glass composition maycontain SiO₂ in an amount less than or equal to 15.0 mol. %, less thanor equal to 14.0 mol. %, less than or equal to 13.0 mol. %, less than orequal to 12.0 mol. %, less than or equal to 10.0 mol. %, less than orequal to 5.0 mol. %, less than or equal to 3.0 mol. %, less than orequal to 2.0 mol. %, less than or equal to 1.0 mol. %, less than orequal to 0.9 mol. %, or less than or equal to 0.8 mol. %. In some moreembodiments, the glass composition may contain SiO₂ in an amount greaterthan or equal to 0.0 mol. % and less than or equal to 1.0 mol. %,greater than or equal to 0.0 mol. % and less than or equal to 0.9 mol.%, greater than or equal to 0.0 mol. % and less than or equal to 0.8mol. %, greater than or equal to 0.0 mol. % and less than or equal to15.0 mol. %, greater than or equal to 0.0 mol. % and less than or equalto 12.0 mol. %, greater than or equal to 0.0 mol. % and less than orequal to 3.0 mol. %, greater than or equal to 0.8 mol. % and less thanor equal to 12.0 mol. %, greater than or equal to 0.8 mol. % and lessthan or equal to 0.9 mol. %, greater than or equal to 0.9 mol. % andless than or equal to 12.0 mol. %, greater than or equal to 1.0 mol. %and less than or equal to 13.0 mol. %, greater than or equal to 1.0 mol.% and less than or equal to 10.0 mol. %, greater than or equal to 2.0mol. % and less than or equal to 13.0 mol. %, greater than or equal to3.0 mol. % and less than or equal to 13.0 mol. %, greater than or equalto 3.0 mol. % and less than or equal to 10.0 mol. %, greater than orequal to 3.0 mol. % and less than or equal to 9.5 mol. %, greater thanor equal to 7.0 mol. % and less than or equal to 11.0 mol. %, or greaterthan or equal to 4.5 mol. % and less than or equal to 9.0 mol. %.

Glass composition may include divalent metal oxides (RO). Divalent metaloxides, such as alkaline earth metal oxides (BeO, MgO, CaO, SrO andBaO), zinc oxide (ZnO), cadmium oxide (CdO), lead oxide (PbO) andothers, being added to a glass, provide comparably high refractiveindexes, greater than those for most of monovalent oxides. Some divalentmetal oxides, such as, for example, CaO, SrO and ZnO, also providecomparably low density, therefore, increasing the ratio of therefractive index to density and, accordingly, improving the performanceof optical glasses in certain applications. In addition, divalent metaloxides may help to increase the solubility of high index components,such as TiO₂, Nb₂O₅ and WO₃, which indirectly leads to a furtherincrease in the refractive index at a comparable density. Also, somedivalent metal oxides, such as, for example, ZnO and MgO, providecomparably low thermal expansion coefficient, which may reduce thethermal stresses formed in the glass articles when cooling and,therefore, improve the quality of the glass articles. However, whenadding at high amounts, divalent metal oxides may cause crystallizationof refractory minerals from the melts or liquid-liquid phase separation,which may reduce the glass-forming ability of glasses. Also, somedivalent metal oxides, such as, for example, PbO and CdO, may cause someecological concern. Accordingly, the amount of divalent metal oxides inglass compositions of the present disclosure is limited.

In some embodiments, the glass composition may contain divalent metaloxides in an amount greater than or equal to 4.0 mol. %.

Glass composition may include calcium oxide (CaO). Calcium oxideprovides the highest ratio of the refractive index to density of glassesamong the known monovalent and divalent metal oxides. Also, in someembodiments, CaO may help to increase the solubility of Nb₂O₅ and TiO₂,which additionally contributes to an increase in refractive index atcomparably low density. However, if the amount of CaO in a glass is toohigh, it may cause crystallization of refractory species, such ascalcium titanates (CaTiO₃, CaTi₂O₅, etc.) calcium niobate (CaNb₂O₆),calcium metasilicate (CaSiO₃) and others, which may reduce the viscosityat the liquidus temperature and, therefore, increase the criticalcooling rate, which may cause crystallization of the glass-forming meltwhen cooling. That is why the amount of CaO in glasses of the presentdisclosure is limited. In embodiments, the glass may contain calciumoxide (CaO) in an amount from greater than or equal to 0.0 mol. % toless than or equal to 35.0 mol. % and all ranges and sub-ranges betweenthe foregoing values. In some embodiments, the glass composition maycontain CaO in an amount greater than or equal to 0.0 mol. %, greaterthan or equal to 0.3 mol. %, greater than or equal to 0.5 mol. %,greater than or equal to 1.0 mol. %, greater than or equal to 2.0 mol.%, greater than or equal to 3.0 mol. %, greater than or equal to 4.0mol. %, greater than or equal to 5.0 mol. %, greater than or equal to5.3 mol. %, greater than or equal to 5.5 mol. %, greater than or equalto 10.0 mol. %, greater than or equal to 15.0 mol. %, greater than orequal to 20.0 mol. %, greater than or equal to 25.0 mol. %, greater thanor equal to 30.0 mol. %, greater than or equal to 32.0 mol. %, greaterthan or equal to 33.0 mol. %, or greater than or equal to 34.0 mol. %.In some other embodiments, the glass composition may contain CaO in anamount less than or equal to 35.0 mol. %, less than or equal to 34.0mol. %, less than or equal to 33.0 mol. %, less than or equal to 32.0mol. %, less than or equal to 30.0 mol. %, less than or equal to 25.0mol. %, less than or equal to 23.0 mol. %, less than or equal to 20.5mol. %, less than or equal to 20.0 mol. %, less than or equal to 15.0mol. %, less than or equal to 14.5 mol. %, less than or equal to 10.0mol. %, less than or equal to 5.0 mol. %, less than or equal to 3.0 mol.%, less than or equal to 2.0 mol. %, or less than or equal to 1.0 mol.%. In some more embodiments, the glass composition may contain CaO in anamount greater than or equal to 0.0 mol. % and less than or equal to14.5 mol. %, greater than or equal to 0.3 mol. % and less than or equalto 30.0 mol. %, greater than or equal to 1.0 mol. % and less than orequal to 35.0 mol. %, greater than or equal to 2.0 mol. % and less thanor equal to 30.0 mol. %, greater than or equal to 4.0 mol. % and lessthan or equal to 23.0 mol. %, greater than or equal to 5.3 mol. % andless than or equal to 15.0 mol. %, greater than or equal to 5.5 mol. %and less than or equal to 20.5 mol. %, greater than or equal to 0.0 mol.% and less than or equal to 35.0 mol. %, greater than or equal to 0.0mol. % and less than or equal to 25.0 mol. %, greater than or equal to0.0 mol. % and less than or equal to 1.0 mol. %, greater than or equalto 1.0 mol. % and less than or equal to 14.5 mol. %, greater than orequal to 2.0 mol. % and less than or equal to 5.0 mol. %, greater thanor equal to 3.0 mol. % and less than or equal to 30.0 mol. %, greaterthan or equal to 3.0 mol. % and less than or equal to 5.0 mol. %,greater than or equal to 5.0 mol. % and less than or equal to 30.0 mol.%, greater than or equal to 5.0 mol. % and less than or equal to 20.0mol. %, greater than or equal to 10.0 mol. % and less than or equal to35.0 mol. %, greater than or equal to 10.0 mol. % and less than or equalto 23.0 mol. %, greater than or equal to 10.0 mol. % and less than orequal to 15.0 mol. %, greater than or equal to 14.5 mol. % and less thanor equal to 23.0 mol. %, greater than or equal to 14.5 mol. % and lessthan or equal to 15.0 mol. %, greater than or equal to 15.0 mol. % andless than or equal to 35.0 mol. %, greater than or equal to 15.0 mol. %and less than or equal to 23.0 mol. %, greater than or equal to 20.0mol. % and less than or equal to 30.0 mol. %, greater than or equal to20.0 mol. % and less than or equal to 23.0 mol. %, greater than or equalto 20.5 mol. % and less than or equal to 35.0 mol. %, greater than orequal to 20.5 mol. % and less than or equal to 33.0 mol. %, greater thanor equal to 20.5 mol. % and less than or equal to 23.0 mol. %, greaterthan or equal to 23.0 mol. % and less than or equal to 33.0 mol. %,greater than or equal to 23.0 mol. % and less than or equal to 30.0 mol.%, greater than or equal to 5.0 mol. % and less than or equal to 18.0mol. %, greater than or equal to 11.0 mol. % and less than or equal to25.0 mol. %, or greater than or equal to 15.0 mol. % and less than orequal to 28.0 mol. %.

Glass composition may include barium oxide (BaO). Barium oxide mayincrease the solubility of high index components, such as TiO₂ andNb₂O₅, more than other divalent metal oxides, which may indirectly leadto a further increase in the refractive index at comparably low density.However, barium is a heavy element and, being added in a high amount,may increase the density of glass. Also, at high concentration, it maycause crystallization of such minerals as barium titanate (BaTiO₃),barium niobate (BaNb₂O₆), barium orthophosphate (Ba₃P₂O₈) and others,which may cause crystallization of a melt when cooling. Accordingly, theamount of BaO in glasses of the present disclosure is limited, orglasses may be substantially free of BaO. In embodiments, the glass maycontain barium oxide (BaO) in an amount from greater than or equal to0.0 mol. % to less than or equal to 15.0 mol. % and all ranges andsub-ranges between the foregoing values. In some embodiments, the glasscomposition may contain BaO in an amount greater than or equal to 0.0mol. %, greater than or equal to 3.0 mol. %, greater than or equal to5.0 mol. %, greater than or equal to 6.0 mol. %, or greater than orequal to 10.0 mol. %. In some other embodiments, the glass compositionmay contain BaO in an amount less than or equal to 15.0 mol. %, lessthan or equal to 17.0 mol. %, less than or equal to 15.0 mol. %, lessthan or equal to 14.5 mol. %, less than or equal to 13.0 mol. %, lessthan or equal to 10.0 mol. %, less than or equal to 8.0 mol. %, or lessthan or equal to 5.0 mol. %. In some more embodiments, the glasscomposition may contain BaO in an amount greater than or equal to 0.0mol. % and less than or equal to 20.0 mol. %, greater than or equal to0.0 mol. % and less than or equal to 15.0 mol. %, greater than or equalto 0.0 mol. % and less than or equal to 14.5 mol. %, greater than orequal to 0.0 mol. % and less than or equal to 13.0 mol. %, greater thanor equal to 3.3 mol. % and less than or equal to 8.01 mol. %, greaterthan or equal to 6.0 mol. % and less than or equal to 17.0 mol. %,greater than or equal to 5.0 mol. % and less than or equal to 15.0 mol.%, greater than or equal to 5.0 mol. % and less than or equal to 13.0mol. %, greater than or equal to 5.0 mol. % and less than or equal to8.0 mol. %, greater than or equal to 8.0 mol. % and less than or equalto 13.0 mol. %, greater than or equal to 10.0 mol. % and less than orequal to 17.0 mol. %, greater than or equal to 10.0 mol. % and less thanor equal to 15.0 mol. %, greater than or equal to 10.0 mol. % and lessthan or equal to 13.0 mol. %, greater than or equal to 13.0 mol. % andless than or equal to 15.0 mol. %, greater than or equal to 13.0 mol. %and less than or equal to 14.5 mol. %, greater than or equal to 4.8 mol.% and less than or equal to 14.3 mol. %, greater than or equal to 7.8mol. % and less than or equal to 14.5 mol. %, or greater than or equalto 5.2 mol. % and less than or equal to 11.1 mol. %.

Glass composition may include magnesia (MgO). Magnesia is not frequentlyused in the high-index optical glasses. Magnesia reduces the thermalexpansion coefficient, which may be useful for reduction of thermalstresses formed in the glass articles when cooling them. However,magnesia provides a lower refractive index and a lower increase in thesolubility of high index components than other divalent metal oxides,such as, for example, BaO, SrO, CaO and ZnO. Also, in phosphate glasses,adding MgO may cause crystallization of magnesium phosphate Mg₃P₂O₈,which may reduce the glass-forming ability of glasses. Accordingly, theamount of MgO in glass compositions of the present disclosure islimited, or glasses may be substantially free of MgO. In embodiments,the glass may contain magnesia (MgO) in an amount from greater than orequal to 0.0 mol. % to less than or equal to 15.0 mol. % and all rangesand sub-ranges between the foregoing values. In some embodiments, theglass composition may contain MgO in an amount greater than or equal to0.0 mol. %, greater than or equal to 1.0 mol. %, greater than or equalto 2.0 mol. %, greater than or equal to 3.0 mol. %, greater than orequal to 5.0 mol. %, greater than or equal to 10.0 mol. %, greater thanor equal to 12.0 mol. %, greater than or equal to 13.0 mol. %, orgreater than or equal to 14.0 mol. %. In some other embodiments, theglass composition may contain MgO in an amount less than or equal to15.0 mol. %, less than or equal to 14.0 mol. %, less than or equal to13.0 mol. %, less than or equal to 12.0 mol. %, less than or equal to10.0 mol. %, less than or equal to 5.0 mol. %, less than or equal to 3.0mol. %, less than or equal to 2.5 mol. %, less than or equal to 2.0 mol.%, or less than or equal to 1.0 mol. %. In some more embodiments, theglass composition may contain MgO in an amount greater than or equal to0.0 mol. % and less than or equal to 15.0 mol. %, greater than or equalto 0.0 mol. % and less than or equal to 2.5 mol. %, greater than orequal to 0.0 mol. % and less than or equal to 3.0 mol. %, greater thanor equal to 0.0 mol. % and less than or equal to 1.0 mol. %, greaterthan or equal to 1.0 mol. % and less than or equal to 15.0 mol. %,greater than or equal to 1.0 mol. % and less than or equal to 12.0 mol.%, greater than or equal to 1.0 mol. % and less than or equal to 3.0mol. %, greater than or equal to 2.0 mol. % and less than or equal to13.0 mol. %, greater than or equal to 2.0 mol. % and less than or equalto 3.0 mol. %, greater than or equal to 2.5 mol. % and less than orequal to 15.0 mol. %, greater than or equal to 2.5 mol. % and less thanor equal to 13.0 mol. %, greater than or equal to 2.5 mol. % and lessthan or equal to 10.0 mol. %, greater than or equal to 2.5 mol. % andless than or equal to 3.0 mol. %, greater than or equal to 3.0 mol. %and less than or equal to 15.0 mol. %, greater than or equal to 3.0 mol.% and less than or equal to 13.0 mol. %, greater than or equal to 5.0mol. % and less than or equal to 15.0 mol. %, greater than or equal to5.0 mol. % and less than or equal to 12.0 mol. %, greater than or equalto 5.1 mol. % and less than or equal to 13.0 mol. %, greater than orequal to 9.5 mol. % and less than or equal to 14.3 mol. %, or greaterthan or equal to 3.9 mol. % and less than or equal to 9.3 mol. %.

Glass composition may include sodium oxide (Na₂O). In high-indexglasses, Na₂O acts like K₂O, improving the solubility of high indexcomponents, such as TiO₂, Nb₂O₅, WO₃ and others, but, at the same time,decreasing the refractive index of glasses. In most cases, the effect ofNa₂O on the solubility of high index components was found to be slightlylower than the corresponding effect of K₂O. However, Na₂O provides alower thermal expansion coefficient than K₂O, which may reduce thethermal stresses formed when cooling the glass articles and, therefore,improve the quality of the articles. In embodiments, the glass maycontain sodium oxide (Na₂O) in an amount from greater than or equal to0.0 mol. % to less than or equal to 15.0 mol. % and all ranges andsub-ranges between the foregoing values. In some embodiments, the glasscomposition may contain Na₂O in an amount greater than or equal to 0.0mol. %, greater than or equal to 5.0 mol. %, or greater than or equal to10.0 mol. %. In some other embodiments, the glass composition maycontain Na₂O in an amount less than or equal to 15.0 mol. %, less thanor equal to 15.0 mol. %, less than or equal to 13.5 mol. %, less than orequal to 12.0 mol. %, less than or equal to 10.5 mol. %, less than orequal to 10.0 mol. %, less than or equal to 7.0 mol. %, or less than orequal to 5.0 mol. %. In some more embodiments, the glass composition maycontain Na₂O in an amount greater than or equal to 0.0 mol. % and lessthan or equal to 20.0 mol. %, greater than or equal to 0.0 mol. % andless than or equal to 15.0 mol. %, greater than or equal to 0.0 mol. %and less than or equal to 13.5 mol. %, greater than or equal to 0.0 mol.% and less than or equal to 12.0 mol. %, greater than or equal to 0.0mol. % and less than or equal to 10.5 mol. %, greater than or equal to0.02 mol. % and less than or equal to 6.98 mol. %, greater than or equalto 5.0 mol. % and less than or equal to 10.5 mol. %, greater than orequal to 5.0 mol. % and less than or equal to 7.0 mol. %, greater thanor equal to 7.0 mol. % and less than or equal to 13.5 mol. %, greaterthan or equal to 7.0 mol. % and less than or equal to 10.5 mol. %,greater than or equal to 5.6 mol. % and less than or equal to 11.0 mol.%, greater than or equal to 2.1 mol. % and less than or equal to 13.0mol. %, or greater than or equal to 5.2 mol. % and less than or equal to9.0 mol. %.

Glass composition may include alumina (Al₂O₃). Alumina may increase theviscosity of glass-forming melts at high temperature, which may reducethe critical cooling rate and improve the glass—forming ability.However, in high-index phosphate glasses, addition of Al₂O₃ may causecrystallization of refractory minerals, such as aluminum phosphate(AlPO₄), aluminum titanate (Al₂TiO₅), aluminum niobate (AlNbO₄) andothers, in the glass-forming melts when cooling. Accordingly, the amountof Al₂O₃ in glasses of the present disclosure is limited, or glasses maybe substantially free of Al₂O₃. In embodiments, the glass may containalumina (Al₂O₃) in an amount from greater than or equal to 0.0 mol. % toless than or equal to 10.0 mol. % and all ranges and sub-ranges betweenthe foregoing values. In some embodiments, the glass composition maycontain Al₂O₃ in an amount greater than or equal to 0.0 mol. %, greaterthan or equal to 0.5 mol. %, greater than or equal to 1.0 mol. %,greater than or equal to 1.5 mol. %, greater than or equal to 2.5 mol.%, greater than or equal to 5.0 mol. %, greater than or equal to 7.5mol. %, greater than or equal to 8.5 mol. %, greater than or equal to9.0 mol. %, or greater than or equal to 9.5 mol. %. In some otherembodiments, the glass composition may contain Al₂O₃ in an amount lessthan or equal to 10.0 mol. %, less than or equal to 9.5 mol. %, lessthan or equal to 9.0 mol. %, less than or equal to 8.5 mol. %, less thanor equal to 7.5 mol. %, less than or equal to 5.0 mol. %, less than orequal to 2.5 mol. %, less than or equal to 1.5 mol. %, less than orequal to 1.0 mol. %, or less than or equal to 0.5 mol. %. In some moreembodiments, the glass composition may contain Al₂O₃ in an amountgreater than or equal to 0.0 mol. % and less than or equal to 10.0 mol.%, greater than or equal to 0.0 mol. % and less than or equal to 8.5mol. %, greater than or equal to 0.0 mol. % and less than or equal to0.5 mol. %, greater than or equal to 0.5 mol. % and less than or equalto 2.5 mol. %, greater than or equal to 1.0 mol. % and less than orequal to 9.0 mol. %, greater than or equal to 1.0 mol. % and less thanor equal to 7.5 mol. %, greater than or equal to 1.0 mol. % and lessthan or equal to 2.5 mol. %, greater than or equal to 1.5 mol. % andless than or equal to 9.0 mol. %, greater than or equal to 2.5 mol. %and less than or equal to 7.5 mol. %, greater than or equal to 5.0 mol.% and less than or equal to 8.5 mol. %, greater than or equal to 5.0mol. % and less than or equal to 7.5 mol. %, greater than or equal to7.5 mol. % and less than or equal to 9.5 mol. %, greater than or equalto 7.5 mol. % and less than or equal to 9.0 mol. %, greater than orequal to 7.5 mol. % and less than or equal to 8.5 mol. %, greater thanor equal to 1.2 mol. % and less than or equal to 9.6 mol. %, greaterthan or equal to 3.5 mol. % and less than or equal to 9.0 mol. %, orgreater than or equal to 4.0 mol. % and less than or equal to 8.0 mol.%.

Glass composition may include vanadia (V₂O₅). Vanadia provides thehighest ratio of the refractive index to density among all oxides.However, vanadia may cause undesirable dark or even black coloring andmay also raise environmental concerns. For these reasons, the content ofvanadia in the glasses of the present disclosure is limited, or glasscompositions may be free of V₂O₅. In embodiments, the glass may containvanadia (V₂O₅) in an amount from greater than or equal to 0.0 mol. % toless than or equal to 1.0 mol. % and all ranges and sub-ranges betweenthe foregoing values. In some embodiments, the glass composition maycontain V₂O₅ in an amount greater than or equal to 0.0 mol. %, greaterthan or equal to 0.05 mol. %, greater than or equal to 0.10 mol. %,greater than or equal to 0.15 mol. %, greater than or equal to 0.25 mol.%, greater than or equal to 0.5 mol. %, greater than or equal to 0.75mol. %, greater than or equal to 0.85 mol. %, greater than or equal to0.9 mol. %, or greater than or equal to 0.95 mol. %. In some otherembodiments, the glass composition may contain V₂O₅ in an amount lessthan or equal to 1.0 mol. %, less than or equal to 0.95 mol. %, lessthan or equal to 0.9 mol. %, less than or equal to 0.85 mol. %, lessthan or equal to 0.75 mol. %, less than or equal to 0.5 mol. %, lessthan or equal to 0.25 mol. %, less than or equal to 0.15 mol. %, lessthan or equal to 0.10 mol. %, or less than or equal to 0.05 mol. %. Insome more embodiments, the glass composition may contain V₂O₅ in anamount greater than or equal to 0.0 mol. % and less than or equal to 1.0mol. %, greater than or equal to 0.0 mol. % and less than or equal to0.85 mol. %, greater than or equal to 0.0 mol. % and less than or equalto 0.25 mol. %, greater than or equal to 0.0 mol. % and less than orequal to 0.05 mol. %, greater than or equal to 0.05 mol. % and less thanor equal to 0.85 mol. %, greater than or equal to 0.05 mol. % and lessthan or equal to 0.25 mol. %, greater than or equal to 0.10 mol. % andless than or equal to 1.0 mol. %, greater than or equal to 0.10 mol. %and less than or equal to 0.9 mol. %, greater than or equal to 0.10 mol.% and less than or equal to 0.75 mol. %, greater than or equal to 0.10mol. % and less than or equal to 0.25 mol. %, greater than or equal to0.15 mol. % and less than or equal to 0.75 mol. %, greater than or equalto 0.15 mol. % and less than or equal to 0.25 mol. %, greater than orequal to 0.25 mol. % and less than or equal to 0.9 mol. %, greater thanor equal to 0.5 mol. % and less than or equal to 1.0 mol. %, greaterthan or equal to 0.5 mol. % and less than or equal to 0.95 mol. %,greater than or equal to 0.5 mol. % and less than or equal to 0.9 mol.%, greater than or equal to 0.75 mol. % and less than or equal to 0.95mol. %, greater than or equal to 0.75 mol. % and less than or equal to0.9 mol. %, greater than or equal to 0.75 mol. % and less than or equalto 0.85 mol. %, greater than or equal to 0.4 mol. % and less than orequal to 0.77 mol. %, greater than or equal to 0.45 mol. % and less thanor equal to 0.85 mol. %, or greater than or equal to 0.56 mol. % andless than or equal to 0.94 mol. %.

Glass composition may include tungsten oxide (WO₃). WO₃ provides highrefractive index without significantly increasing density or causingundesirable coloring. However, at high concentrations of WO₃, such asgreater than or equal to 10.0 mol. %, or greater than or equal to 20.0mol. %, the liquidus temperature tends to rise, and the viscosity at theliquidus temperature drops, making it difficult to avoid crystallizationof melts when cooling and/or to obtain high-quality optical glass.Accordingly, the content of WO₃ should be limited, or glass compositionsmay be free of WO₃. In embodiments, the glass may contain tungsten oxide(WO₃) in an amount from greater than or equal to 0.0 mol. % to less thanor equal to 10.0 mol. % and all ranges and sub-ranges between theforegoing values. In some embodiments, the glass composition may containWO₃ in an amount greater than or equal to 0.0 mol. %, greater than orequal to 2.5 mol. %, greater than or equal to 3.0 mol. %, greater thanor equal to 5.0 mol. %, or greater than or equal to 7.5 mol. %. In someother embodiments, the glass composition may contain WO₃ in an amountless than or equal to 10.0 mol. %, less than or equal to 8.5 mol. %,less than or equal to 7.5 mol. %, less than or equal to 6.0 mol. %, lessthan or equal to 5.0 mol. %, less than or equal to 4.6 mol. %, or lessthan or equal to 2.5 mol. %. In some more embodiments, the glasscomposition may contain WO₃ in an amount greater than or equal to 0.0mol. % and less than or equal to 10.0 mol. %, greater than or equal to0.0 mol. % and less than or equal to 8.5 mol. %, greater than or equalto 0.0 mol. % and less than or equal to 7.5 mol. %, greater than orequal to 0.0 mol. % and less than or equal to 4.6 mol. %, greater thanor equal to 2.5 mol. % and less than or equal to 6.15 mol. %, greaterthan or equal to 0.0 mol. % and less than or equal to 5.0 mol. %,greater than or equal to 0.0 mol. % and less than or equal to 2.5 mol.%, greater than or equal to 2.5 mol. % and less than or equal to 10.0mol. %, greater than or equal to 2.5 mol. % and less than or equal to7.5 mol. %, greater than or equal to 2.5 mol. % and less than or equalto 5.0 mol. %, greater than or equal to 4.6 mol. % and less than orequal to 10.0 mol. %, greater than or equal to 4.6 mol. % and less thanor equal to 8.5 mol. %, greater than or equal to 4.6 mol. % and lessthan or equal to 7.5 mol. %, greater than or equal to 4.6 mol. % andless than or equal to 6.0 mol. %, greater than or equal to 4.6 mol. %and less than or equal to 5.0 mol. %, greater than or equal to 5.0 mol.% and less than or equal to 10.0 mol. %, greater than or equal to 5.0mol. % and less than or equal to 8.5 mol. %, greater than or equal to5.0 mol. % and less than or equal to 7.5 mol. %, greater than or equalto 5.0 mol. % and less than or equal to 6.0 mol. %, greater than orequal to 3.2 mol. % and less than or equal to 7.9 mol. %, greater thanor equal to 3.0 mol. % and less than or equal to 8.5 mol. %, or greaterthan or equal to 2.2 mol. % and less than or equal to 6.3 mol. %.

Glass composition may include tantalum oxide (Ta₂O₅). Tantalum oxideincreases the refractive index while maintaining an acceptable densitywithout reducing the blue transmittance. However, when added to a glasscomposition, sometimes even in small amounts, Ta₂O₅ may causecrystallization of refractory minerals, which may increase the liquidustemperature and, therefore, reduce the glass-forming ability.Accordingly, the content of tantalum oxide should be limited, or glasscompositions may be free of Ta₂O₅. In embodiments, the glass may containtantalum oxide (Ta₂O₅) in an amount from greater than or equal to 0.0mol. % to less than or equal to 5.0 mol. % and all ranges and sub-rangesbetween the foregoing values. In some embodiments, the glass compositionmay contain Ta₂O₅ in an amount greater than or equal to 0.0 mol. %,greater than or equal to 0.02 mol. %, greater than or equal to 1.0 mol.%, greater than or equal to 2.0 mol. %, greater than or equal to 3.0mol. %, or greater than or equal to 4.0 mol. %. In some otherembodiments, the glass composition may contain Ta₂O₅ in an amount lessthan or equal to 5.0 mol. %, less than or equal to 4.0 mol. %, less thanor equal to 3.0 mol. %, less than or equal to 2.0 mol. %, less than orequal to 1.8 mol. %, less than or equal to 1.6 mol. %, less than orequal to 1.0 mol. %, or less than or equal to 0.03 mol. %. In some moreembodiments, the glass composition may contain Ta₂O₅ in an amountgreater than or equal to 0.0 mol. % and less than or equal to 2.0 mol.%, greater than or equal to 0.0 mol. % and less than or equal to 1.8mol. %, greater than or equal to 0.0 mol. % and less than or equal to1.6 mol. %, greater than or equal to 0.02 mol. % and less than or equalto 0.03 mol. %, greater than or equal to 0.0 mol. % and less than orequal to 5.0 mol. %, greater than or equal to 0.0 mol. % and less thanor equal to 1.0 mol. %, greater than or equal to 0.03 mol. % and lessthan or equal to 3.0 mol. %, greater than or equal to 0.03 mol. % andless than or equal to 1.8 mol. %, greater than or equal to 1.0 mol. %and less than or equal to 5.0 mol. %, greater than or equal to 1.0 mol.% and less than or equal to 3.0 mol. %, greater than or equal to 1.0mol. % and less than or equal to 1.8 mol. %, greater than or equal to1.6 mol. % and less than or equal to 5.0 mol. %, greater than or equalto 1.6 mol. % and less than or equal to 4.0 mol. %, greater than orequal to 1.6 mol. % and less than or equal to 3.0 mol. %, greater thanor equal to 1.8 mol. % and less than or equal to 5.0 mol. %, greaterthan or equal to 1.8 mol. % and less than or equal to 3.0 mol. %,greater than or equal to 1.8 mol. % and less than or equal to 2.0 mol.%, greater than or equal to 1.0 mol. % and less than or equal to 4.0mol. %, greater than or equal to 1.0 mol. % and less than or equal to3.0 mol. %, or greater than or equal to 3.0 mol. % and less than orequal to 4.0 mol. %.

Glass composition may include bismuth oxide (Bi₂O₃). Bi₂O₃ provides veryhigh refractive index, higher than any other components consideredherein, but leads to increases in density. Sometimes it may provideundesirable coloring. Also, it may decrease the viscosity of melts athigh temperatures, which may cause crystallization of the melts whencooling. This effect is especially significant at high concentrations ofBi₂O₃, such as, for example, greater than 20.0 mol. %, or greater than26.0 mol. %, or higher. Accordingly, the content of bismuth oxide shouldbe limited, or glass compositions may be free of Bi₂O₃. In embodiments,the glass may contain bismuth oxide (Bi₂O₃) in an amount from greaterthan or equal to 0.0 mol. % to less than or equal to 10.0 mol. % and allranges and sub-ranges between the foregoing values. In some embodiments,the glass composition may contain Bi₂O₃ in an amount greater than orequal to 0.0 mol. %, greater than or equal to 1.0 mol. %, greater thanor equal to 2.5 mol. %, greater than or equal to 5.0 mol. %, or greaterthan or equal to 7.5 mol. %. In some other embodiments, the glasscomposition may contain Bi₂O₃ in an amount less than or equal to 10.0mol. %, less than or equal to 7.5 mol. %, less than or equal to 5.0 mol.%, less than or equal to 4.6 mol. %, less than or equal to 4.0 mol. %,less than or equal to 3.4 mol. %, less than or equal to 3.0 mol. %, orless than or equal to 2.5 mol. %. In some more embodiments, the glasscomposition may contain Bi₂O₃ in an amount greater than or equal to 0.0mol. % and less than or equal to 4.6 mol. %, greater than or equal to0.0 mol. % and less than or equal to 4.0 mol. %, greater than or equalto 0.0 mol. % and less than or equal to 3.4 mol. %, greater than orequal to 0.0 mol. % and less than or equal to 3.0 mol. %, greater thanor equal to 1.43 mol. % and less than or equal to 3.62 mol. %, greaterthan or equal to 0.0 mol. % and less than or equal to 10.0 mol. %,greater than or equal to 2.5 mol. % and less than or equal to 5.0 mol.%, greater than or equal to 2.5 mol. % and less than or equal to 4.0mol. %, greater than or equal to 2.5 mol. % and less than or equal to3.0 mol. %, greater than or equal to 3.0 mol. % and less than or equalto 5.0 mol. %, greater than or equal to 3.0 mol. % and less than orequal to 4.0 mol. %, greater than or equal to 3.4 mol. % and less thanor equal to 7.5 mol. %, greater than or equal to 3.4 mol. % and lessthan or equal to 5.0 mol. %, greater than or equal to 3.4 mol. % andless than or equal to 4.6 mol. %, greater than or equal to 3.4 mol. %and less than or equal to 4.0 mol. %, greater than or equal to 5.8 mol.% and less than or equal to 9.2 mol. %, greater than or equal to 0.9mol. % and less than or equal to 5.7 mol. %, or greater than or equal to1.1 mol. % and less than or equal to 5.6 mol. %.

Glass composition may include lithium oxide (Li₂O). Lithium oxideprovides the highest ratio of the refractive index to density of glassesamong the known monovalent metal oxides. Also, in some embodiments, Li₂Omay help to increase the solubility of Nb₂O₅ and TiO₂, whichadditionally increases the refractive index at comparably low density.In addition, lithium oxide may hasten the process of bleaching theglasses. However, it was empirically found that in some embodiments,addition of Li₂O, even in small concentrations, may decrease theglass-forming ability of glasses by causing crystallization orliquid-liquid phase separation of glass-forming melts when cooling.Therefore, the amount of Li₂O in glasses of the present disclosure islimited. However, the mentioned undesirable effects of Li₂O aredifficult to predict; for this reason, the exact boundary of Li₂O in theembodiments may be very different. In particular, in some embodiments,the glasses may be substantially free of Li₂O. In embodiments, the glassmay contain lithium oxide (Li₂O) in an amount from greater than or equalto 0.0 mol. % to less than or equal to 10.0 mol. % and all ranges andsub-ranges between the foregoing values. In some embodiments, the glasscomposition may contain Li₂O in an amount greater than or equal to 0.0mol. %, greater than or equal to 0.5 mol. %, greater than or equal to1.0 mol. %, greater than or equal to 1.5 mol. %, greater than or equalto 2.5 mol. %, greater than or equal to 5.0 mol. %, greater than orequal to 7.5 mol. %, greater than or equal to 8.5 mol. %, greater thanor equal to 9.0 mol. %, or greater than or equal to 9.5 mol. %. In someother embodiments, the glass composition may contain Li₂O in an amountless than or equal to 10.0 mol. %, less than or equal to 9.5 mol. %,less than or equal to 9.0 mol. %, less than or equal to 8.5 mol. %, lessthan or equal to 7.5 mol. %, less than or equal to 6.0 mol. %, less thanor equal to 5.0 mol. %, less than or equal to 4.5 mol. %, less than orequal to 4.0 mol. %, less than or equal to 3.0 mol. %, less than orequal to 2.5 mol. %, less than or equal to 1.5 mol. %, less than orequal to 1.0 mol. %, or less than or equal to 0.5 mol. %. In some moreembodiments, the glass composition may contain Li₂O in an amount greaterthan or equal to 0.0 mol. % and less than or equal to 6.0 mol. %,greater than or equal to 0.0 mol. % and less than or equal to 5.0 mol.%, greater than or equal to 0.0 mol. % and less than or equal to 4.5mol. %, greater than or equal to 0.0 mol. % and less than or equal to4.0 mol. %, greater than or equal to 0.99 mol. % and less than or equalto 3.0 mol. %, greater than or equal to 0.0 mol. % and less than orequal to 10.0 mol. %, greater than or equal to 0.0 mol. % and less thanor equal to 7.5 mol. %, greater than or equal to 0.5 mol. % and lessthan or equal to 10.0 mol. %, greater than or equal to 0.5 mol. % andless than or equal to 7.5 mol. %, greater than or equal to 0.5 mol. %and less than or equal to 4.0 mol. %, greater than or equal to 1.0 mol.% and less than or equal to 4.0 mol. %, greater than or equal to 1.5mol. % and less than or equal to 8.5 mol. %, greater than or equal to1.5 mol. % and less than or equal to 5.0 mol. %, greater than or equalto 2.5 mol. % and less than or equal to 8.5 mol. %, greater than orequal to 2.5 mol. % and less than or equal to 3.0 mol. %, greater thanor equal to 3.0 mol. % and less than or equal to 8.5 mol. %, greaterthan or equal to 3.0 mol. % and less than or equal to 5.0 mol. %,greater than or equal to 4.0 mol. % and less than or equal to 9.0 mol.%, greater than or equal to 4.0 mol. % and less than or equal to 7.5mol. %, greater than or equal to 4.0 mol. % and less than or equal to5.0 mol. %, greater than or equal to 5.4 mol. % and less than or equalto 9.9 mol. %, greater than or equal to 3.5 mol. % and less than orequal to 8.1 mol. %, or greater than or equal to 0.3 mol. % and lessthan or equal to 5.6 mol. %.

Glass composition may include potassium oxide (K₂O). Potassium oxide mayincrease the solubility of high index components, such as TiO₂ andNb₂O₅, more than other monovalent and divalent metal oxides, which mayindirectly increase the refractive index at comparably low density.However, potassium oxide itself provides the lowest refractive indexamong the mentioned oxides. Therefore, at high concentrations of K₂O, itmay be difficult to reach high refractive index. Accordingly, the amountof K₂O in glasses of the present disclosure is limited, or glasses maybe substantially free of K₂O. In embodiments, the glass may containpotassium oxide (K₂O) in an amount from greater than or equal to 0.3mol. % to less than or equal to 35.0 mol. % and all ranges andsub-ranges between the foregoing values. In some embodiments, the glasscomposition may contain K₂O in an amount greater than or equal to 0.3mol. %, greater than or equal to 0.5 mol. %, greater than or equal to1.0 mol. %, greater than or equal to 2.0 mol. %, greater than or equalto 3.0 mol. %, greater than or equal to 4.0 mol. %, greater than orequal to 5.0 mol. %, greater than or equal to 10.0 mol. %, greater thanor equal to 15.0 mol. %, greater than or equal to 20.0 mol. %, greaterthan or equal to 25.0 mol. %, greater than or equal to 30.0 mol. %,greater than or equal to 32.0 mol. %, greater than or equal to 33.0 mol.%, or greater than or equal to 34.0 mol. %. In some other embodiments,the glass composition may contain K₂O in an amount less than or equal to35.0 mol. %, less than or equal to 34.0 mol. %, less than or equal to33.0 mol. %, less than or equal to 32.0 mol. %, less than or equal to30.0 mol. %, less than or equal to 25.0 mol. %, less than or equal to20.0 mol. %, less than or equal to 16.0 mol. %, less than or equal to15.0 mol. %, less than or equal to 14.5 mol. %, less than or equal to13.8 mol. %, less than or equal to 13.5 mol. %, less than or equal to10.0 mol. %, less than or equal to 5.0 mol. %, less than or equal to 3.0mol. %, less than or equal to 2.0 mol. %, or less than or equal to 1.0mol. %. In some more embodiments, the glass composition may contain K₂Oin an amount greater than or equal to 0.3 mol. % and less than or equalto 20.0 mol. %, greater than or equal to 1.0 mol. % and less than orequal to 35.0 mol. %, greater than or equal to 2.0 mol. % and less thanor equal to 13.5 mol. %, greater than or equal to 4.0 mol. % and lessthan or equal to 20.0 mol. %, greater than or equal to 4.0 mol. % andless than or equal to 16.0 mol. %, greater than or equal to 5.0 mol. %and less than or equal to 14.5 mol. %, greater than or equal to 5.0 mol.% and less than or equal to 13.81 mol. %, greater than or equal to 0.3mol. % and less than or equal to 35.0 mol. %, greater than or equal to0.3 mol. % and less than or equal to 25.0 mol. %, greater than or equalto 0.3 mol. % and less than or equal to 13.8 mol. %, greater than orequal to 0.3 mol. % and less than or equal to 2.0 mol. %, greater thanor equal to 1.0 mol. % and less than or equal to 25.0 mol. %, greaterthan or equal to 1.0 mol. % and less than or equal to 13.8 mol. %,greater than or equal to 1.0 mol. % and less than or equal to 2.0 mol.%, greater than or equal to 2.0 mol. % and less than or equal to 25.0mol. %, greater than or equal to 2.0 mol. % and less than or equal to13.8 mol. %, greater than or equal to 3.0 mol. % and less than or equalto 30.0 mol. %, greater than or equal to 3.0 mol. % and less than orequal to 15.0 mol. %, greater than or equal to 3.0 mol. % and less thanor equal to 10.0 mol. %, greater than or equal to 5.0 mol. % and lessthan or equal to 35.0 mol. %, greater than or equal to 5.0 mol. % andless than or equal to 30.0 mol. %, greater than or equal to 5.0 mol. %and less than or equal to 10.0 mol. %, greater than or equal to 10.0mol. % and less than or equal to 30.0 mol. %, greater than or equal to10.0 mol. % and less than or equal to 15.0 mol. %, greater than or equalto 13.5 mol. % and less than or equal to 32.0 mol. %, greater than orequal to 13.5 mol. % and less than or equal to 20.0 mol. %, greater thanor equal to 13.5 mol. % and less than or equal to 14.5 mol. %, greaterthan or equal to 13.8 mol. % and less than or equal to 35.0 mol. %,greater than or equal to 13.8 mol. % and less than or equal to 20.0 mol.%, greater than or equal to 13.8 mol. % and less than or equal to 14.5mol. %, greater than or equal to 14.5 mol. % and less than or equal to35.0 mol. %, greater than or equal to 14.5 mol. % and less than or equalto 32.0 mol. %, greater than or equal to 14.5 mol. % and less than orequal to 20.0 mol. %, greater than or equal to 5.0 mol. % and less thanor equal to 14.0 mol. %, greater than or equal to 3.0 mol. % and lessthan or equal to 23.0 mol. %, or greater than or equal to 4.0 mol. % andless than or equal to 15.0 mol. %.

Glass composition may include titania (TiO₂). High refractive indexglasses typically include species, such as TiO₂ and Nb₂O₅, that absorbat least a portion of optical light, particularly light in the blue andnear-UV regions of the electromagnetic spectrum. In embodiments of thepresent disclosure, the transmittance of the glass may be characterizedfor different wavelengths within the range of from about 300 nm to 2300nm. High transmission in the visible and near-UV range (blue region) isparticularly desirable in some applications. High transmittance in theblue can be challenging to achieve in high refractive index glasses.High levels of TiO₂ and/or Nb₂O₅ that are typically used in glasses toincrease refractive index tend to decrease the transmittance in thenear-UV region and shift the UV cut-off to higher wavelengths.Accordingly, the amount of TiO₂ in the glass compositions of the presentdisclosure is limited. In embodiments, the glass may contain titania(TiO₂) in an amount from greater than or equal to 0.3 mol. % to lessthan or equal to 50.0 mol. % and all ranges and sub-ranges between theforegoing values. In some embodiments, the glass composition may containTiO₂ in an amount greater than or equal to 0.3 mol. %, greater than orequal to 1.0 mol. %, greater than or equal to 2.0 mol. %, greater thanor equal to 4.0 mol. %, greater than or equal to 6.0 mol. %, greaterthan or equal to 9.0 mol. %, greater than or equal to 10.0 mol. %,greater than or equal to 12.0 mol. %, greater than or equal to 13.0 mol.%, greater than or equal to 15.0 mol. %, greater than or equal to 20.0mol. %, greater than or equal to 30.0 mol. %, greater than or equal to40.0 mol. %, greater than or equal to 44.0 mol. %, greater than or equalto 46.0 mol. %, or greater than or equal to 48.0 mol. %. In some otherembodiments, the glass composition may contain TiO₂ in an amount lessthan or equal to 50.0 mol. %, less than or equal to 48.0 mol. %, lessthan or equal to 46.0 mol. %, less than or equal to 44.0 mol. %, lessthan or equal to 40.0 mol. %, less than or equal to 37.0 mol. %, lessthan or equal to 34.0 mol. %, less than or equal to 33.0 mol. %, lessthan or equal to 30.0 mol. %, less than or equal to 26.0 mol. %, lessthan or equal to 20.0 mol. %, less than or equal to 10.0 mol. %, lessthan or equal to 6.0 mol. %, less than or equal to 4.0 mol. %, or lessthan or equal to 2.0 mol. %. In some more embodiments, the glasscomposition may contain TiO₂ in an amount greater than or equal to 0.3mol. % and less than or equal to 40.0 mol. %, greater than or equal to1.0 mol. % and less than or equal to 50.0 mol. %, greater than or equalto 6.0 mol. % and less than or equal to 40.0 mol. %, greater than orequal to 9.0 mol. % and less than or equal to 37.0 mol. %, greater thanor equal to 12.0 mol. % and less than or equal to 34.0 mol. %, greaterthan or equal to 13.0 mol. % and less than or equal to 33.0 mol. %,greater than or equal to 15.0 mol. % and less than or equal to 26.39mol. %, greater than or equal to 0.3 mol. % and less than or equal to50.0 mol. %, greater than or equal to 2.0 mol. % and less than or equalto 40.0 mol. %, greater than or equal to 2.0 mol. % and less than orequal to 30.0 mol. %, greater than or equal to 4.0 mol. % and less thanor equal to 50.0 mol. %, greater than or equal to 4.0 mol. % and lessthan or equal to 40.0 mol. %, greater than or equal to 4.0 mol. % andless than or equal to 30.0 mol. %, greater than or equal to 6.0 mol. %and less than or equal to 50.0 mol. %, greater than or equal to 10.0mol. % and less than or equal to 50.0 mol. %, greater than or equal to10.0 mol. % and less than or equal to 44.0 mol. %, greater than or equalto 10.0 mol. % and less than or equal to 34.0 mol. %, greater than orequal to 10.0 mol. % and less than or equal to 26.0 mol. %, greater thanor equal to 20.0 mol. % and less than or equal to 44.0 mol. %, greaterthan or equal to 20.0 mol. % and less than or equal to 34.0 mol. %,greater than or equal to 20.0 mol. % and less than or equal to 26.0 mol.%, greater than or equal to 26.0 mol. % and less than or equal to 44.0mol. %, greater than or equal to 26.0 mol. % and less than or equal to34.0 mol. %, greater than or equal to 30.0 mol. % and less than or equalto 50.0 mol. %, greater than or equal to 30.0 mol. % and less than orequal to 46.0 mol. %, greater than or equal to 30.0 mol. % and less thanor equal to 40.0 mol. %, greater than or equal to 30.0 mol. % and lessthan or equal to 34.0 mol. %, greater than or equal to 33.0 mol. % andless than or equal to 46.0 mol. %, greater than or equal to 33.0 mol. %and less than or equal to 40.0 mol. %, greater than or equal to 33.0mol. % and less than or equal to 34.0 mol. %, greater than or equal to22.0 mol. % and less than or equal to 46.0 mol. %, greater than or equalto 16.0 mol. % and less than or equal to 34.0 mol. %, or greater than orequal to 10.0 mol. % and less than or equal to 40.0 mol. %.

Glass composition may include niobia (Nb₂O₅). Niobia, like titania, canbe used in some aspects of the present disclosure to increase therefractive index of glass while also maintaining a low density. However,niobia can introduce a yellow coloring to the glass that cannot bebleached in the same manner as titania, which can result in a loss oftransmittance, particularly in the blue and UV range. Niobia, liketitania, may cause crystallization and/or phase separation of the melt.In some cases, niobia may provide the glass with a high opticaldispersion, which can be significantly higher than that induced bytitania and some other high index components, when added in similarconcentrations. The effects of niobia can be affected by the othercomponents of the glass, and thus it can be challenging to determine anexact limit for niobia. In some embodiments, the glasses may besubstantially free of Nb₂O₅; in this case, its function is performed byother species, such as, for example, TiO₂. In embodiments, the glass maycontain niobia (Nb₂O₅) in an amount from greater than or equal to 0.0mol. % to less than or equal to 50.0 mol. % and all ranges andsub-ranges between the foregoing values. In some embodiments, the glasscomposition may contain Nb₂O₅ in an amount greater than or equal to 0.0mol. %, greater than or equal to 2.0 mol. %, greater than or equal to4.0 mol. %, greater than or equal to 6.0 mol. %, greater than or equalto 10.0 mol. %, greater than or equal to 13.0 mol. %, greater than orequal to 16.0 mol. %, greater than or equal to 20.0 mol. %, greater thanor equal to 21.0 mol. %, greater than or equal to 30.0 mol. %, greaterthan or equal to 40.0 mol. %, greater than or equal to 44.0 mol. %,greater than or equal to 46.0 mol. %, or greater than or equal to 48.0mol. %. In some other embodiments, the glass composition may containNb₂O₅ in an amount less than or equal to 50.0 mol. %, less than or equalto 48.0 mol. %, less than or equal to 46.0 mol. %, less than or equal to44.0 mol. %, less than or equal to 40.0 mol. %, less than or equal to38.0 mol. %, less than or equal to 35.0 mol. %, less than or equal to30.0 mol. %, less than or equal to 20.0 mol. %, less than or equal to10.0 mol. %, less than or equal to 6.0 mol. %, less than or equal to 4.0mol. %, or less than or equal to 2.0 mol. %. In some more embodiments,the glass composition may contain Nb₂O₅ in an amount greater than orequal to 0.0 mol. % and less than or equal to 50.0 mol. %, greater thanor equal to 10.0 mol. % and less than or equal to 40.0 mol. %, greaterthan or equal to 13.0 mol. % and less than or equal to 38.0 mol. %,greater than or equal to 16.0 mol. % and less than or equal to 35.0 mol.%, greater than or equal to 20.29 mol. % and less than or equal to 34.59mol. %, greater than or equal to 21.0 mol. % and less than or equal to35.0 mol. %, greater than or equal to 0.0 mol. % and less than or equalto 40.0 mol. %, greater than or equal to 0.0 mol. % and less than orequal to 20.0 mol. %, greater than or equal to 0.0 mol. % and less thanor equal to 2.0 mol. %, greater than or equal to 2.0 mol. % and lessthan or equal to 40.0 mol. %, greater than or equal to 4.0 mol. % andless than or equal to 44.0 mol. %, greater than or equal to 6.0 mol. %and less than or equal to 35.0 mol. %, greater than or equal to 6.0 mol.% and less than or equal to 10.0 mol. %, greater than or equal to 10.0mol. % and less than or equal to 44.0 mol. %, greater than or equal to10.0 mol. % and less than or equal to 35.0 mol. %, greater than or equalto 20.0 mol. % and less than or equal to 50.0 mol. %, greater than orequal to 20.0 mol. % and less than or equal to 40.0 mol. %, greater thanor equal to 30.0 mol. % and less than or equal to 46.0 mol. %, greaterthan or equal to 30.0 mol. % and less than or equal to 40.0 mol. %,greater than or equal to 30.0 mol. % and less than or equal to 35.0 mol.%, greater than or equal to 35.0 mol. % and less than or equal to 50.0mol. %, greater than or equal to 35.0 mol. % and less than or equal to46.0 mol. %, greater than or equal to 35.0 mol. % and less than or equalto 40.0 mol. %, greater than or equal to 38.0 mol. % and less than orequal to 48.0 mol. %, greater than or equal to 38.0 mol. % and less thanor equal to 44.0 mol. %, greater than or equal to 38.0 mol. % and lessthan or equal to 40.0 mol. %, greater than or equal to 37.0 mol. % andless than or equal to 49.0 mol. %, greater than or equal to 25.0 mol. %and less than or equal to 46.0 mol. %, or greater than or equal to 7.0mol. % and less than or equal to 25.0 mol. %.

In some embodiments, the glass composition may have a sum of SiO₂+GeO₂greater than or equal to 0.0 mol. %, greater than or equal to 5.0 mol.%, or greater than or equal to 10.0 mol. %. In some other embodiments,the glass composition may have a sum of SiO₂+GeO₂ less than or equal to15.0 mol. %, less than or equal to 10.0 mol. %, or less than or equal to5.0 mol. %. In some more embodiments, the glass composition may have asum of SiO₂+GeO_(z) greater than or equal to 0.0 mol. % and less than orequal to 15.0 mol. %, greater than or equal to 0.0 mol. % and less thanor equal to 10.0 mol. %, greater than or equal to 0.0 mol. % and lessthan or equal to 5.0 mol. %, greater than or equal to 5.0 mol. % andless than or equal to 15.0 mol. %, greater than or equal to 5.0 mol. %and less than or equal to 10.0 mol. %, greater than or equal to 3.0 mol.% and less than or equal to 12.0 mol. %, greater than or equal to 6.2mol. % and less than or equal to 11.3 mol. %, or greater than or equalto 3.0 mol. % and less than or equal to 9.0 mol. %.

In some embodiments, the glass composition may have a sum ofTeO₂+SnO₂+SnO greater than or equal to 0.0 mol. %, greater than or equalto 5.0 mol. %, greater than or equal to 10.0 mol. %, or greater than orequal to 15.0 mol. %. In some other embodiments, the glass compositionmay have a sum of TeO₂+SnO₂+SnO less than or equal to 20.0 mol. %, lessthan or equal to 15.0 mol. %, less than or equal to 10.0 mol. %, or lessthan or equal to 5.0 mol. %. In some more embodiments, the glasscomposition may have a sum of TeO₂+SnO₂+SnO greater than or equal to 0.0mol. % and less than or equal to 20.0 mol. %, greater than or equal to0.0 mol. % and less than or equal to 15.0 mol. %, greater than or equalto 0.0 mol. % and less than or equal to 10.0 mol. %, greater than orequal to 0.0 mol. % and less than or equal to 5.0 mol. %, greater thanor equal to 5.0 mol. % and less than or equal to 20.0 mol. %, greaterthan or equal to 5.0 mol. % and less than or equal to 15.0 mol. %,greater than or equal to 5.0 mol. % and less than or equal to 10.0 mol.%, greater than or equal to 10.0 mol. % and less than or equal to 20.0mol. %, greater than or equal to 10.0 mol. % and less than or equal to15.0 mol. %, greater than or equal to 3.0 mol. % and less than or equalto 14.0 mol. %, greater than or equal to 6.0 mol. % and less than orequal to 15.0 mol. %, or greater than or equal to 7.0 mol. % and lessthan or equal to 15.0 mol. %.

In some embodiments, the glass may have a refractive index n_(d) fromgreater than or equal to 1.75 to less than or equal to 2.06 and allranges and sub-ranges between the foregoing values. In some embodiments,the glass composition may have a refractive index n_(d) greater than orequal to 1.75, greater than or equal to 1.76, greater than or equal to1.78, greater than or equal to 1.80, greater than or equal to 1.85,greater than or equal to 1.91, greater than or equal to 1.95, greaterthan or equal to 2.00, greater than or equal to 2.02, greater than orequal to 2.04, or greater than or equal to 2.05. In some otherembodiments, the glass composition may have a refractive index n_(d)less than or equal to 2.06, less than or equal to 2.05, less than orequal to 2.04, less than or equal to 2.02, less than or equal to 2.00,less than or equal to 1.98, less than or equal to 1.95, less than orequal to 1.85, less than or equal to 1.80, less than or equal to 1.78,or less than or equal to 1.76. In some more embodiments, the glasscomposition may have a refractive index n_(d) greater than or equal to1.75 to 2.06, greater than or equal to 1.75 to 2.02, greater than orequal to 1.76 to 2.06, greater than or equal to 1.76 to 2.02, greaterthan or equal to 1.76 to 1.95, greater than or equal to 1.78 to 2.06,greater than or equal to 1.78 to 2.02, greater than or equal to 1.78 to1.95, greater than or equal to 1.80 to 2.04, greater than or equal to1.80 to 2.00, greater than or equal to 1.80 to 1.95, greater than orequal to 1.85 to 2.06, greater than or equal to 1.85 to 2.04, greaterthan or equal to 1.85 to 2.00, greater than or equal to 1.85 to 1.95,greater than or equal to 1.95 to 2.04, greater than or equal to 1.98 to2.05, greater than or equal to 1.98 to 2.04, greater than or equal to1.90 to 2.03, greater than or equal to 1.88 to 2.04, or greater than orequal to 1.91 to 2.03.

In some embodiments, the glass composition may have a density d_(RT)less than or equal to 4.2 g/cm³. In some other embodiments, the glasscomposition may have a density d_(RT) less than or equal to 4.2 g/cm³,less than or equal to 4.0 g/cm³, or less than or equal to 3.8 g/cm³.

In some embodiments, the glass composition may have a refraction((n_(d)−1)/d_(RT)) greater than or equal to 0.24.In some embodiments,the glass composition may have a refraction ((n_(d)−1)/d_(RT)) greaterthan or equal to 0.24, or greater than or equal to 0.25.

In some embodiments, the glass composition may have a quantityn_(d)−(1.54+0.1*d_(RT)) greater than or equal to 0.00.

In some embodiments, the glass composition may have a quantityn_(d)−(1.58+0.1*d_(RT)) greater than or equal to 0.00.

In some other embodiments, the glass composition may have a quantityν_(d)−(64.5−23.4*n_(d)) less than or equal to 0.00.

In some other embodiments, the glass composition may have a quantityν_(d)−(63.7−23.4*n_(d)) less than or equal to 0.00.

Refractive index n_(d), density d_(RT), Abbe number ν_(d) and refractionare properties of a glass that can be predicted from the glasscomposition. A linear regression analysis of the exemplary glasses ofthe present disclosure in the EXAMPLES section below and other glasscompositions reported in the literature was performed to determineequations that can predict the composition dependences of refractiveindex n_(d), density d_(RT), Abbe number ν_(d) and refraction.

The training dataset of glass compositions satisfying the criteriaspecified in Table 1 below and having measured values of the propertiesof interest, about 100 glass compositions for each property (n_(d),d_(RT), ν_(d), and refraction), was randomly selected from theliterature data presented in the publicly available SciGlass InformationSystem database and from the Exemplary Glasses from the embodimentspresented herein. The linear regression analysis on the above-specifieddataset was used to determine the formulas, with the exclusion ofinsignificant variables and outliers. The resulting formulas arepresented in Table 2 below. Another part of glass compositionssatisfying the same criteria was used as a validation set to evaluatethe ability to interpolate within predefined compositional limits, whichcorresponds to the standard deviations specified in the Table 2. Anexternal dataset of prior art glass compositions, also randomly selectedfrom the SciGlass Information System database, was used to evaluate theability to predict the properties outside of the specified compositionallimits with a reasonable accuracy. Multiple iterations of this processwere performed in order to determine the best variant for each property,corresponding to the above-mentioned regression formulas specified inthe Table 2.

The data for the Comparative Glass compositions used in the linearregression modeling, including the training dataset, validation datasetand external dataset were obtained from the publicly available SciGlassInformation System database. Formulas (I), (II), (111) and (IV) belowwere obtained from the linear regression analysis and used to predictthe refractive index n_(d), density d_(RT), Abbe number ν_(d), andrefraction, respectively, of the glasses:

P_(n)=−0.0043794*P₂O₅+0.0072428*Nb₂O₅+0.0037304*TiO₂−0.00039553*BaO−0.0032012*K₂O−0.00060689*CaO−0.0024218*Na₂O−0.0014988*Li₂O+0.0028587*WO₃+0.0083295*Bi₂O₃−0.0031637*B₂O₃−0.0030702*SiO₂−0.00030248*ZnO+0.0020025*ZrO₂−0.0018173*MgO−0.0032886*Al₂O₃+0.0024221*TeO₂+0.0038137*PbO−0.0016392*GeO₂+0.0063024*Tl₂O+0.0048765*Ag₂O+1.81451,  (I)

P_(d)[g/cm³]=3.98457−0.015773*Al₂O₃−0.014501*B₂O₃+0.019328*BaO+0.060758*Bi₂O₃−0.0012685*CaO+0.023111*CdO+0.0053184*Cs₂O+0.011488*Ga₂O₃−0.0015416*GeO₂−0.013342*K₂O+0.058319*La₂O₃−0.007918*Li₂O−0.0021423*MgO−0.0024413*MoO₃−0.0082226*Na₂O+0.0084961*Nb₂O₅−0.020501*P₂O₅+0.038898*PbO−0.012720*SiO₂+0.013948*SrO+0.047924*Ta₂O₅+0.011248*TeO₂−0.0092491*V₂O₅+0.028913*WO₃+0.0074702*ZnO+0.0096721*ZrO₂,  (II)

P_(ν)=exp(2.11+0.0438*(exp(3.25980+0.0072248*Al₂O₃+0.0055494*B₂O₃+0.0024164*BaO−0.00849*Bi₂O₃+0.0029812*CaO+0.0092768*CdO+0.0099821*Ga₂O₃−0.0038579*GeO₂+0.0028062*K₂O+0.0031951*Li₂O+0.0027011*MgO+0.007976*MoO₃+0.0028705*Na₂O−0.013374*Nb₂O₅+0.0072007*P₂O₅−0.0049796*PbO+0.0032241*SiO₂+0.0050024*SrO−0.002136*Ta₂O₅−0.0032329*TeO₂−0.009788*TiO₂+0.0074782*V₂O₅−0.0057095*WO₃+0.0032826*ZnO+0.009302*ZrO₂))),  (III)

P_(ref)[cm³/g]=0.223637+0.0010703*Nb₂O₅−0.00041688*P₂O₅+0.00088482*TiO₂+0.000054956*CaO−0.00029243*K₂O−0.0008347*BaO−0.00023739*Na₂O+0.000082792*Li₂O−0.0012487*WO₃−0.00042393*ZnO−0.00059152*SrO−0.00018266*MgO−0.0014091*Bi₂O₃−0.0014895*Ta₂O₅−0.00021842*SiO₂−0.00024788*ZrO₂−0.00014801*B₂O₃−0.000060848*TeO₂−0.00085564*PbO−0.00042429*GeO₂−0.0015439*Tl₂O−0.0012936*Ag₂O−0.00089356*Cu₂O−0.00039278*CuO+0.00017895*As₂O₃−0.00011802*Sb₂O₃.  (IV)

In Formulas (I), (II), (III) and (IV) and Tables 1 and 2, refractiveindex parameter P_(n) is a parameter that predicts the refractive indexn_(d) from the concentrations of the components of the glass compositionexpressed in mol. %; density parameter P_(d) is a parameter thatpredicts the density d_(RT) from the concentrations of the components ofthe glass composition expressed in mol. %; dispersion parameter P_(ν) isa parameter that predicts the Abbe number ν_(d) from the concentrationsof the components of the glass composition expressed in mol. %; andP_(ref) is a parameter that predicts the refraction from theconcentrations of the components of the glass composition expressed inmol. %. For dispersion parameter P_(ν), a logarithmic scale was appliedwhen performing the regression analysis. In Formulas (I), (II), (III)and (IV), each component of the glass composition is listed in terms ofits chemical formula, where the chemical formula refers to theconcentration of the component expressed in mol. %. For example, forpurposes of Formulas (I), (II), (III) and (IV), P₂O₅ refers to theconcentration of P₂O₅, expressed in mol. %, in the glass composition. Itis understood that not all components listed in Formulas (I), (II),(III), and (IV) are necessarily present in a particular glasscomposition and that Formulas (I), (II), (III), and (IV) are equallyvalid for glass compositions that contain less than all of thecomponents listed in the formulas. It is further understood thatFormulas (I), (II), (III), and (IV) are also valid for glasscompositions within the scope and claims of the present disclosure thatcontain components in addition to the components listed in the formulas.If a component listed in Formulas (I), (II), (III), and (IV) is absentin a particular glass composition, the concentration of the component inthe glass composition is 0 mol. % and the contribution of the componentto the value calculated from the formulas is zero. In Table 1,R_(m)O_(n) is a total sum of all oxides.

TABLE 1 Composition Space Used for Modeling Property n_(d) d_(RT) ν_(d)(n_(d) − 1)/d_(RT) Min, Max, Min, Max, Min, Max, Min, Max, Componentlimits mol. % mol. % mol. % mol. % mol. % mol. % mol. % mol. % Nb₂O₅ 560 0 60 5 60 5 60 P₂O₅ 10 30 10 30 10 30 10 30 TiO₂ 0 40 0 40 0 40 0 40CaO 0 40 0 40 0 40 0 40 K₂O 0 20 0 20 0 20 0 20 BaO 0 20 0 20 0 20 0 20Na₂O 0 30 0 30 0 30 0 30 SiO₂ 0 20 0 20 0 20 0 20 ZnO 0 20 0 20 0 20 020 Li₂O 0 10 0 10 0 10 0 10 SrO 0 30 0 30 0 30 0 30 ZrO₂ 0 10 0 10 0 100 10 WO₃ 0 15 0 15 0 15 0 15 MgO 0 10 0 10 0 10 0 10 B₂O₃ 0 10 0 10 0 100 10 Al₂O₃ 0  5 0  5 0  5 0  5 R_(m)O_(n) 99 Not 99 Not 99 Not 99 Notlimited limited limited limited TeO₂ + PbO + 0 20 0 20 0 20 0 20 GeO₂ +Tl₂O Ag₂O + Cu₂O + CuO + 0 15 0 15 0 15 0 15 As₂O₃ + Sb₂O₃ P₂O₅—SiO₂ 10Not 10 Not 10 Not 10 Not limited limited limited limited TiO₂ + Nb₂O₅ +WO₃ + 25 Not Not Not Not Not 25 Not GeO₂ + Bi₂O₃ + limited limitedlimited limited limited limited TeO₂ TiO₂ + Nb₂O₅ + WO₃ + Not Not 25 NotNot Not Not Not V₂O₅ + GeO₂ + limited limited limited limited limitedlimited limited Bi₂O₃ + TeO₂ V₂O₅ Not Not 0 80 Not Not Not Not limitedlimited limited limited limited limited Other species 0 Not 0 Not 0 Not0 Not limited limited limited limited

TABLE 2 Property prediction models Predicting Regression StandardProperty Abbreviation Unit Parameter Formula error Refractive n_(d)P_(n) Formula (I) 0.016 index at 587.56 nm Density at d_(RT) g/cm³ P_(d)Formula (II) 0.20 room temperature Abbe ν_(d) P_(ν) Formula (III) 0.66number Refraction (n_(d) − 1)/d_(RT) cm³/g P_(ref) Formula (IV) 0.0049

FIG. 1 is a plot of the parameter P_(n) calculated by Formula (I) as afunction of measured refractive index n_(d) for some Literature Glasses(“Comp. Glasses”) and some Exemplary Glasses (“Ex. Glasses”). Asillustrated by the data in FIG. 1, the compositional dependence of theparameter P_(n) had an error within a range of ±0.016 unit of themeasured n_(d) for the majority of glasses, that corresponds to thestandard error specified in Table 2.

FIG. 2 is a plot of the parameter P_(d) calculated by Formula (II) as afunction of measured density d_(RT) for some Literature Glasses (“Comp.Glasses”) and some Exemplary Glasses (“Ex. Glasses”). As illustrated bythe data in FIG. 2, the compositional dependence of the parameter P_(d)had an error within a range of ±0.20 unit of the measured d_(RT) for themajority of glasses, that corresponds to the standard error specified inTable 2.

FIG. 3 is a plot of the parameter P_(ν) calculated by Formula (III) as afunction of measured Abbe number ν_(d) for some Literature Glasses(“Comp. Glasses”) and some Exemplary Glasses (“Ex. Glasses”). Asillustrated by the data in FIG. 3, the compositional dependence of theparameter P_(ν) had an error within a range of ±0.66 unit of themeasured ν_(d) for the majority of glasses, that corresponds to thestandard error specified in Table 2.

FIG. 4 is a plot of the parameter P_(ref) calculated by Formula (IV) asa function of measured refraction (n_(d)−1)/d_(RT) for some LiteratureGlasses (“Comp. Glasses”) and some Exemplary Glasses (“Ex. Glasses”). Asillustrated by the data in FIG. 4, the compositional dependence of theparameter P_(ref) had an error within a range of ±0.0049 unit of themeasured refraction (n_(d)−1)/d_(RT) for the majority of glasses, thatcorresponds to the standard error specified in Table 2.

Table 3 identifies the combination of components and their respectiveamounts according to some embodiments of the present disclosure. TheExemplary Glasses A in Table 3 may include additional componentsaccording to any aspects of the present disclosure as described herein.

TABLE 3 Exemplary Glasses A Composition Amount (mol. %) P₂O₅ 10.0 to40.0 mol. % TiO₂ 0.5 to 50.0 mol. % K₂O 0.5 to 35.0 mol. % CaO 0.5 to35.0 mol. % Nb₂O₅ 0.0 to 50.0 mol. % MgO 0.0 to 15.0 mol. % Al₂O₃ 0.0 to10.0 mol. % Total sum of divalent metal oxides RO ≥4.0 mol. % Sum of(TeO₂ + SnO₂ + SnO) 0.0 to 20.0 mol. % Sum of (SiO₂ + GeO₂) 0.0 to 15.0mol. %

Exemplary Glasses A according to embodiments of the present disclosuremay satisfy the following formula:

n _(d)−(1.54+0.1*d _(RT))>0.00,

where n_(d) is a refractive index at 587.56 nm, and d_(RT) is a densityat room temperature expressed in units of g/cm³.

According to some embodiments of the present disclosure, ExemplaryGlasses A may also satisfy the following formula:

n _(d)−(1.58+0.1*d _(RT))>0.00,

where n_(d) is a refractive index at 587.56 nm, and d_(RT) is a densityat room temperature expressed in units of g/cm³.

Table 4 identifies the combination of components and their respectiveamounts according to some embodiments of the present disclosure. TheExemplary Glasses B in Table 4 may include additional componentsaccording to any aspects of the present disclosure as described herein.

TABLE 4 Exemplary Glasses B Composition Amount (mol. %) P₂O₅ 10.0 to40.0 mol. % TiO₂ 1.0 to 50.0 mol. % K₂O 1.0 to 35.0 mol. % CaO 1.0 to35.0 mol. % Nb₂O₅ 0.0 to 50.0 mol. % MgO 0.0 to 15.0 mol. % Al₂O₃ 0.0 to10.0 mol. % Total sum of divalent metal oxides RO ≥4.0 mol. % Sum of(TeO₂ + SnO₂ + SnO) 0.0 to 20.0 mol. % Sum of (SiO₂ + GeO₂) 0.0 to 15.0mol. %

Exemplary Glasses B according to embodiments of the present disclosuremay have a refractive index n_(d) of greater than or equal to 1.75.

According to some embodiments of the present disclosure, ExemplaryGlasses B may also satisfy the following formula:

ν_(d)−(64.5−23.4*n _(d))<0.00,

where ν_(d) is an Abbe number, and n_(d) is a refractive index at 587.56nm.

According to some embodiments of the present disclosure, ExemplaryGlasses B may also satisfy the following formula:

ν_(d)−(63.7−23.4*n _(d))<0.00,

where ν_(d) is an Abbe number, and n_(d) is a refractive index at 587.56nm.

EXAMPLES

The following examples describe various features and advantages providedby the disclosure, and are in no way intended to limit the invention andappended claims.

To prepare the glass samples for some exemplary glasses of the presentdisclosure, about 15 grams of each sample (content of target species wasmore than 99.99 wt %) was melted from batch raw materials at atemperature of about 1300° C. in platinum or platinum-rhodium crucibles(Pt:Rh=80:20) for 1 hour. Two controlled cooling conditions wereapplied. In the first condition (referred to as “15 min test” or “15 mindevit test”), the sample was left in the furnace after melting and thefurnace was turned off to allow the sample to cool slowly in air. Underthese conditions, it takes about 15 min for the samples to cool from1100° C. to 500° C. In the second condition (referred to as “2.5 mintest” or “2.5 min devit test”), the furnace was turned off and thesample was removed from the furnace at a temperature of 1100° C. andallowed to cool in air at room temperature. Under these conditions, ittakes about 2.5 min for the samples to cool from 1100° C. to 500° C.Temperature readings were obtained by direct reading of the furnacetemperature or using an IR camera reading with calibration scaling. Thefirst condition (15 min test) approximately corresponds to the coolingrate of up to 300° C./min at a temperature of 1000° C. and the secondtest approximately corresponds to the cooling rate of up to 600° C./minat 1000° C. (near to this temperature, the cooling rate approached themaximum). When the temperature is lower, the cooling rate also decreasessignificantly. Typical schedules of the first and second cooling regimesare shown in FIG. 5. For these samples, observations referred to as“15-min devit test” and “2.5-min devit test”, are specified in Table 5below; the observation “1” is used to denote that a glass compositionpassed the indicated devit test, where a composition is deemed to havepassed the indicated devit test if the volume fraction of the glassypart of the sample is more than that of the crystals. The observation“0” is used to denote that the crystal volume fraction is more than thatof the glassy part.

To prepare other glass samples for exemplary glasses of the presentdisclosure, unless otherwise specified, a one kilogram of batch wasprepared in a pure platinum crucible. The crucible was placed in afurnace set at a temperature of 1250° C., after which, the temperaturein the furnace was raised to 1300° C. and held at 1300° C. for 2 hours.The furnace temperature was then reduced to 1250° C. and the glass wasallowed to equilibrate at this temperature for an hour before beingpoured on a steel table followed by annealing at Tg for an hour. Forsome compositions, slight adjustments to temperatures and times weremade to ensure complete melting. For example, for some compositionsmelting temperatures of 1350° C. or 1400° C. and/or hold times of up to4 hours were used.

Some sample melts were also melted in a “one liter” platinum crucibleheated by Joule effect. In this process, approximately 3700 g of rawmaterials was used. The crucible was filled in 1.5 hours at 1250° C. Thetemperature was then raised to 1300° C. and held for one hour. Duringthis step, the glass was continuously stirred at 60 rpm. The temperaturewas then decreased to 1200° C. where it was allowed to equilibrate for30 minutes and the stirring speed was decreased to 20 rpm. The deliverytube was heated at 1225° C. and the glass was casted on a cooledgraphite table. The glass was formed into a bar of approximately 25 mmin thickness, 50 mm in width, and 90 cm in length. The prepared barswere inspected under an optical microscope to check for crystallizationand were all crystal free. The glass quality observed under the opticalmicroscope was good with the bars being free of striae and bubbles. Theglass was placed at Tg in a lehr oven for 1 hour for a rough annealing.The bars were then annealed in a static furnace for one hour at Tg andthe temperature was then lowered at 1° C./min.

No chemical analysis of the tested samples was performed becausechemical analysis was performed for similar samples prepared inindependent meltings by XRF method (X-ray fluorescence—for all oxides,except for B₂O₃ and Li₂O), by ICP method (inductively coupled plasmamass spectrometry -for B₂O₃) and by FES method (flame emissionspectrometry—for Li₂O). These analyses gave deviations from the batchedcompositions within ±2.0 mass % for the major components such as Nb₂O₅which is equivalently less than about 1 mol %.

In Tables 5 and 6, n_(632.8 nm) and n_(531.9 nm) refer to the refractiveindex at wavelengths of 632.8 nm and 531.9 nm, respectively. T_(x)refers to the crystallization onset temperature.

TABLE 5 Exemplary Glass Compositions Exemplary Glass 1 2 3 4 5 6 7 8Composition - mol. % P₂O₅ mol. % 31.01 29.98 24.95 24.99 25.00 25.0025.00 24.99 Nb₂O₅ mol. % 10.00 34.98 20.96 37.00 36.99 39.00 38.99 34.00TiO₂ mol. % 30.01 10.01 19.96 9.99 10.01 9.99 10.01 15.00 BaO mol. %7.00 0 0 6.00 9.99 4.99 8.00 5.00 Na₂O mol. % 14.96 11.11 0.0639 6.986.97 6.97 6.98 4.98 K₂O mol. % 5.00 6.45 14.98 7.99 8.00 8.00 7.99 5.01CaO mol. % 2.00 7.43 18.97 7.00 2.99 6.01 2.99 6.01 Al₂O₃ mol. % 0.01180.0158 0.0259 0 0 0 0 0 CeO₂ mol. % 0.007 0 0 0 0 0 0 0 Ta₂O₅ mol. %0.0027 0.0328 0.0209 0.034 0.0348 0.0347 0.0353 0.0322 MgO mol. % 0 00.0655 0 0 0 0 0 SrO mol. % 0 0 0 0.0161 0.0165 0 0 0 Li₂O mol. % 0 0 00 0 0 0 4.98 Measured properties n_(d) 1.8068 1.8696 1.966 1.953 1.98421.9686 1.9829 d_(RT) g/cm³ 3.272 3.487 3.808 3.843 3.822 3.835 3.777n_(632.8 nm) 1.7995 1.8604 1.9561 1.9434 1.9738 1.9585 1.9726n_(531.9 nm) 1.8190 1.8852 1.9830 1.9694 2.0021 1.9859 2.0007 n_(F)1.8331 2.0023 1.9882 2.0224 2.0057 2.0210 T_(g) ° C. 624.40 T_(x) ° C.767.60 ν_(d) 22.0 19.1 19.5 18.5 18.8 18.6 (n_(d) − 1)/d_(RT) 0.246570.25367 0.24798 0.25751 0.25256 0.26024 Predicted and calculatedproperties P_(n) [for n_(d)] 1.807 1.922 1.872 1.961 1.962 1.977 1.9771.966 P_(d) [for d_(RT)] g/cm³ 3.377 3.482 3.427 3.732 3.814 3.730 3.7923.704 P_(ν) [for ν_(d)] 22.59 19.57 21.05 18.66 18.62 18.18 18.15 18.47n_(d) − (1.54 + 0.1 * d_(RT)) −0.0709 0.0336 −0.0110 0.0481 0.04070.0637 0.0581 0.0556 n_(d) − (1.58 + 0.1 * d_(RT)) −0.1109 −0.0064−0.0510 0.0081 6.900E−04 0.0237 0.0181 0.0156 ν_(d) − (64.5 − 23.4 *n_(d)) 0.3682 0.0422 0.3460 0.0478 0.0318 −0.0665 −0.0767 −0.0268 ν_(d)− (63.7 − 23.4 * n_(d)) 1.168 0.8422 1.146 0.8478 0.8318 0.7335 0.72330.7732 Exemplary Glass 9 10 11 12 13 14 15 16 Composition - mol. % P₂O₅mol. % 25.00 24.99 24.99 24.99 24.99 24.99 24.09 24.99 Nb₂O₅ mol. %33.99 34.00 36.98 36.98 37.99 37.98 26.07 38.99 TiO₂ mol. % 15.00 15.018.01 5.99 8.01 6.00 20.05 10.00 BaO mol. % 5.00 8.00 9.99 10.00 6.006.00 0 3.00 Na₂O mol. % 6.98 6.98 6.99 6.98 6.98 6.99 0 6.98 K₂O mol. %7.99 8.00 7.99 8.00 8.01 8.00 4.93 8.00 CaO mol. % 6.00 3.01 2.49 2.015.49 5.01 24.84 8.01 Ta₂O₅ mol. % 0.0328 0.0297 0.0356 0.0323 0.03520.036 0.025 0.0381 SrO mol. % 0 0 0.0169 0.0172 0 0 0 0 WO₃ mol. % 0 02.50 5.00 2.50 5.00 0 0 Measured properties n_(d) 1.9612 1.9548 1.9505d_(RT) g/cm³ 3.740 3.777 3.901 3.957 3.852 3.886 3.758 n_(632.8 nm)1.9513 1.9451 1.9405 n_(531.9 nm) 1.9783 1.9716 1.9676 n_(F) 1.99791.9906 1.9872 T_(g) ° C. 673.30 T_(x) ° C. 771.00 ν_(d) 18.9 19.2 18.6(n_(d) − 1)/d_(RT) 0.25701 0.25281 Predicted and calculated propertiesP_(n) [for n_(d)] 1.959 1.960 1.962 1.962 1.969 1.969 1.942 1.976 P_(d)[for d_(RT)] g/cm³ 3.688 3.749 3.887 3.959 3.814 3.887 3.616 3.689 P_(ν)[for ν_(d)] 18.44 18.42 18.68 18.74 18.46 18.53 19.48 18.20 n_(d) −(1.54 + 0.1 * d_(RT)) 0.0503 0.0449 0.0333 0.0260 0.0477 0.0402 0.04010.0673 n_(d) − (1.58 + 0.1 * d_(RT)) 0.0103 0.0049 −0.0067 −0.01400.0077 2.200E−04 1.200E−04 0.0273 ν_(d) − (64.5 − 23.4 * n_(d)) −0.2159−0.2263 0.0902 0.1497 0.0397 0.0982 0.4111 −0.0605 ν_(d) − (63.7 −23.4 * n_(d)) 0.5841 0.5737 0.8902 0.9497 0.8397 0.8982 1.211 0.7395Exemplary Glass 17 18 19 20 21 22 23 24 Composition - mol. % P₂O₅ mol. %25.00 24.49 24.49 24.50 24.30 24.99 25.10 25.10 Nb₂O₅ mol. % 39.00 34.9934.99 34.99 34.99 27.99 33.09 26.06 TiO₂ mol. % 9.99 14.99 15.00 15.0113.00 22.00 13.04 20.06 BaO mol. % 1.00 4.50 2.50 2.50 2.20 0 0 0 Na₂Omol. % 6.98 4.99 4.98 6.97 6.99 0.0232 0.0249 0.0227 K₂O mol. % 8.004.99 5.00 8.01 8.00 5.00 9.93 9.93 CaO mol. % 9.99 6.00 8.00 7.99 7.9919.98 18.79 18.80 Ta₂O₅ mol. % 0.0376 0.0325 0.0321 0.0326 0.0333 0.0260.0314 0.0255 Li₂O mol. % 0 5.02 5.01 0 0 0 0 0 WO₃ mol. % 0 0 0 0 2.500 0 0 Measured properties n_(d) 1.9623 1.9502 1.9303 d_(RT) g/cm³ 3.7293.768 3.734 3.712 3.767 n_(632.8 nm) 1.9510 1.9402 1.9210 n_(531.9 nm)1.9819 1.9683 1.9472 n_(F) 2.0044 1.9875 1.9648 15-min devit test (0/1)1 1 1 Predicted and calculated properties P_(n) [for n_(d)] 1.976 1.9761.975 1.968 1.969 1.962 1.950 1.925 P_(d) [for d_(RT)] g/cm³ 3.648 3.7133.672 3.655 3.726 3.619 3.596 3.536 P_(ν) [for ν_(d)] 18.21 18.21 18.2218.19 18.24 18.64 19.11 19.53 n_(d) − (1.54 + 0.1 * d_(RT)) 0.07110.0643 0.0680 0.0628 0.0563 0.0598 0.0500 0.0313 n_(d) − (1.58 + 0.1 *d_(RT)) 0.0311 0.0243 0.0280 0.0228 0.0163 0.0198 0.0100 −0.0087 ν_(d) −(64.5 − 23.4 * n_(d)) −0.0542 −0.0664 −0.0609 −0.2507 −0.1891 0.03950.2356 0.0732 ν_(d) − (63.7 − 23.4 * n_(d)) 0.7458 0.7336 0.7391 0.54930.6109 0.8395 1.036 0.8732 Exemplary Glass 25 26 27 28 29 30 31 32Composition - mol. % P₂O₅ mol. % 24.98 24.29 23.49 24.29 23.49 24.9924.99 24.99 Nb₂O₅ mol. % 22.98 34.88 35.69 39.87 40.79 39.00 38.99 34.00TiO₂ mol. % 20.00 15.61 16.30 10.59 11.20 10.00 10.01 14.99 BaO mol. % 05.00 5.10 5.00 5.10 6.00 7.00 7.00 Na₂O mol. % 0.0437 4.49 4.08 6.997.09 5.98 4.97 3.98 K₂O mol. % 12.98 5.11 5.10 7.11 6.20 7.00 6.00 4.00CaO mol. % 18.95 6.10 6.09 6.11 6.09 7.00 8.00 8.00 Al₂O₃ mol. % 0.01330 0 0 0 0 0 0 Ta₂O₅ mol. % 0.0215 0.0326 0.0328 0.0388 0.039 0.03480.0349 0.0327 MgO mol. % 0.0336 0 0 0 0 0 0 0 Li₂O mol. % 0 4.49 4.10 00 0 0 3.00 Measured properties n_(d) 1.8937 1.9868 1.9996 1.9843 2.00061.976 1.9806 1.9777 d_(RT) g/cm³ 3.781 3.818 3.819 3.848 3.809n_(632.8 nm) 1.8848 1.9764 1.9888 1.9741 1.9895 1.9659 1.9703 1.9676n_(531.9 nm) 1.9095 2.0042 2.0179 2.0016 2.0192 1.9930 1.9980 1.9947n_(F) 1.9264 (n_(d) − 1)/d_(RT) 0.26098 0.25782 0.25557 0.25484 0.2566815-min devit test (0/1) 1 Predicted and calculated properties P_(n) [forn_(d)] 1.893 1.979 1.993 1.991 2.006 1.981 1.986 1.973 P_(d) [ford_(RT)] g/cm³ 3.471 3.733 3.765 3.764 3.801 3.770 3.809 3.778 P_(ν) [forν_(d)] 20.42 18.10 17.74 17.83 17.48 18.17 18.17 18.45 n_(d) − (1.54 +0.1 * d_(RT)) 0.0058 0.0661 0.0764 0.0747 0.0860 0.0644 0.0650 0.0549n_(d) − (1.58 + 0.1 * d_(RT)) −0.0342 0.0261 0.0364 0.0347 0.0460 0.02440.0250 0.0149 ν_(d) − (64.5 − 23.4 * n_(d)) 0.2097 −0.0829 −0.1229−0.0775 −0.0756 0.0372 0.1410 0.1100 ν_(d) − (63.7 − 23.4 * n_(d)) 1.0100.7171 0.6771 0.7225 0.7244 0.8372 0.9410 0.9100 Exemplary Glass 33 3435 36 37 38 39 40 Composition - mol. % P₂O₅ mol. % 25.00 24.99 25.0024.99 24.29 24.06 23.97 23.92 Nb₂O₅ mol. % 32.50 32.48 32.50 32.48 37.4928.04 27.91 26.85 TiO₂ mol. % 20.00 20.01 20.00 20.01 10.99 22.04 21.9420.89 BaO mol. % 5.70 2.50 5.70 2.50 2.10 0 5.92 7.90 Na₂O mol. % 3.984.00 3.98 4.00 4.49 0.0232 0.70 0.94 K₂O mol. % 4.00 4.00 4.00 4.00 5.107.95 7.86 7.85 CaO mol. % 5.80 9.00 5.80 9.00 7.99 17.86 11.66 11.64Ta₂O₅ mol. % 0.0284 0.0314 0.0284 0.0314 0.0339 0.0261 0.027 0.0236 Li₂Omol. % 3.00 2.99 3.00 2.99 4.52 0 0 0 WO₃ mol. % 0 0 0 0 3.00 0 0 0Measured properties n_(d) 1.9888 1.9901 1.989 1.9902 1.9922 d_(RT) g/cm³3.761 3.710 3.766 3.712 3.824 3.665 3.734 3.728 n_(632.8 nm) 1.97801.9793 1.9782 1.9795 1.9816 n_(531.9 nm) 2.0075 2.0088 2.0077 2.00862.0106 n_(F) 2.0289 2.0302 2.0290 2.0296 2.0317 T_(g) ° C. 677.30 677.10674.20 T_(x) ° C. 765.30 773.50 783.00 ν_(d) 17.8 17.8 17.8 18.1 18.1(n_(d) − 1)/d_(RT) 0.26291 0.26688 0.26262 0.26675 0.25947 15-min devittest (0/1) 1 1 1 Predicted and calculated properties P_(n) [for n_(d)]1.982 1.982 1.982 1.982 1.990 1.958 1.957 1.945 P_(d) [for d_(RT)] g/cm³3.742 3.677 3.742 3.677 3.783 3.602 3.721 3.749 P_(ν) [for ν_(d)] 17.9017.92 17.90 17.92 17.99 18.55 18.54 19.00 n_(d) − (1.54 + 0.1 * d_(RT))0.0681 0.0738 0.0681 0.0738 0.0713 0.0579 0.0452 0.0297 n_(d) − (1.58 +0.1 * d_(RT)) 0.0281 0.0338 0.0281 0.0338 0.0313 0.0179 0.0052 −0.0103ν_(d) − (64.5 − 23.4 * n_(d)) −0.2188 −0.2097 −0.2188 −0.2097 0.0415−0.1315 −0.1584 −5.300E−05 ν_(d) − (63.7 − 23.4 * n_(d)) 0.5812 0.59030.5812 0.5903 0.8415 0.6685 0.6416 0.7999 Exemplary Glass 41 42 43 44 4546 47 48 Composition - mol. % P₂O₅ mol. % 24.70 25.00 25.00 25.00 25.0024.99 25.00 25.00 Nb₂O₅ mol. % 34.59 32.50 32.51 32.51 32.49 32.48 29.9927.50 TiO₂ mol. % 9.89 21.00 21.00 20.01 20.00 20.00 24.00 28.00 BaOmol. % 9.86 5.70 5.70 4.70 5.21 4.70 4.21 5.71 Na₂O mol. % 1.16 3.993.98 3.99 3.99 4.00 3.98 3.98 K₂O mol. % 4.94 4.00 4.01 4.00 4.01 4.014.00 4.01 CaO mol. % 14.82 5.81 4.80 4.79 5.30 4.80 5.80 2.81 Ta₂O₅ mol.% 0.0334 0 0 2.00 0 0 0.0274 0.0269 Li₂O mol. % 0 2.00 3.00 3.01 3.013.02 2.99 2.98 Bi₂O₃ mol. % 0 0 0 0 1.00 2.00 0 0 Measured propertiesn_(d) 1.9993 1.9976 2.0021 2.0014 2.0086 1.9905 1.949 d_(RT) g/cm³ 3.8313.777 3.769 3.854 3.835 3.898 3.690 3.602 n_(632.8 nm) 1.9885 1.98681.9913 1.9905 1.9975 1.9791 1.9386 n_(531.9 nm) 2.0181 2.0163 2.02102.0203 2.0279 2.0104 1.9669 n_(F) 2.0395 2.0377 2.0425 2.0418 2.04982.0332 1.9873 ν_(d) 17.9 18.0 17.9 17.9 17.7 16.8 17.8 (n_(d) −1)/d_(RT) 0.26458 0.26469 0.26003 0.26113 0.25876 0.26843 0.26346Predicted and calculated properties P_(n) [for n_(d)] 1.962 1.988 1.9871.983 1.991 2.000 1.980 1.978 P_(d) [for d_(RT)] g/cm³ 3.870 3.749 3.7423.819 3.793 3.844 3.692 3.704 P_(ν) [for ν_(d)] 19.26 17.72 17.72 17.7617.75 17.60 17.77 17.62 n_(d) − (1.54 + 0.1 * d_(RT)) 0.0352 0.07260.0724 0.0615 0.0717 0.0753 0.0705 0.0674 n_(d) − (1.58 + 0.1 * d_(RT))−0.0048 0.0326 0.0324 0.0215 0.0317 0.0353 0.0305 0.0274 ν_(d) − (64.5 −23.4 * n_(d)) 0.6781 −0.2728 −0.2919 −0.3279 −0.1649 −0.1086 −0.4076−0.6023 ν_(d) − (63.7 − 23.4 * n_(d)) 1.478 0.5272 0.5081 0.4721 0.63510.6914 0.3924 0.1977 Exemplary Glass 49 50 51 52 53 54 55 56Composition - mol. % P₂O₅ mol. % 24.99 24.99 24.99 23.34 23.33 23.2824.79 23.35 Nb₂O₅ mol. % 29.31 28.49 27.67 31.96 31.95 31.91 29.94 30.96TiO₂ mol. % 29.31 28.50 27.67 20.96 20.96 20.95 21.85 21.97 BaO mol. % 00 0 6.99 7.98 7.48 6.26 7.99 Na₂O mol. % 0 0 0 0 0 2.65 4.24 0 K₂O mol.% 11.78 8.83 5.89 8.49 5.49 3.99 4.62 6.50 CaO mol. % 4.59 9.16 13.768.24 8.26 7.73 8.19 7.21 Al₂O₃ mol. % 0 0 0 0 0 0 0.0148 0 Ta₂O₅ mol. %0.0273 0.0267 0.0262 0.0287 0.0285 0.0283 0.0277 0.0283 SrO mol. % 0 0 00 0 0 0.054 0 Li₂O mol. % 0 0 0 0 2.00 1.99 0 1.99 Fe₂O₃ mol. % 0 0 0 00 0 0.0028 0 Measured properties n_(d) 2.001 1.9818 d_(RT) g/cm³ 3.5553.578 3.597 3.811 3.849 3.706 3.796 n_(632.8 nm) 1.9901 1.9711n_(531.9 nm) 2.0196 2.0001 n_(F) 2.0417 2.0218 T_(liq) ° C. 1175.01180.0 1205.0 1150.0 1170.0 ν_(d) 17.8 17.8 (n_(d) − 1)/d_(RT) 0.262660.26493 Predicted and calculated properties P_(n) [for n_(d)] 1.9861.984 1.982 1.987 1.993 1.992 1.972 1.987 P_(d) [for d_(RT)] g/cm³ 3.5603.586 3.613 3.790 3.834 3.824 3.747 3.813 P_(ν) [for ν_(d)] 17.04 17.3517.67 17.73 17.74 17.75 18.13 17.78 n_(d) − (1.54 + 0.1 * d_(RT)) 0.09020.0853 0.0802 0.0680 0.0698 0.0696 0.0571 0.0658 n_(d) − (1.58 + 0.1 *d_(RT)) 0.0502 0.0453 0.0402 0.0280 0.0298 0.0296 0.0171 0.0258 ν_(d) −(64.5 − 23.4 * n_(d)) −0.9800 −0.7278 −0.4604 −0.2748 −0.1237 −0.1397−0.2355 −0.2223 ν_(d) − (63.7 − 23.4 * n_(d)) −0.1800 0.0722 0.33960.5252 0.6763 0.6603 0.5645 0.5777 Exemplary Glass 57 58 59 60 61 62 6364 Composition - mol. % P₂O₅ mol. % 23.34 24.98 24.98 24.98 24.98 24.9924.47 24.98 Nb₂O₅ mol. % 30.61 19.99 20.99 19.49 18.29 18.29 23.18 26.19TiO₂ mol. % 22.27 23.99 25.19 27.29 29.28 29.29 25.99 22.00 BaO mol. %6.89 7.70 4.80 4.70 4.54 0 0 0 Na₂O mol. % 2.80 0.0222 0.0223 0.02190.0215 0.0208 0.0222 0 K₂O mol. % 4.13 13.49 17.19 16.79 16.27 16.2915.20 15.99 CaO mol. % 7.89 7.79 4.81 4.71 4.60 9.11 10.10 8.79 Al₂O₃mol. % 0.0148 0 0 0 0 0 0 0 Ta₂O₅ mol. % 0.0277 0.0187 0.0188 0.01840.0181 0.0175 0.0218 0.0227 SrO mol. % 0.0568 0 0 0 0 0 0 0 Li₂O mol. %1.97 2.02 1.99 1.99 2.00 1.98 1.01 2.02 Fe₂O₃ mol. % 0.0038 0 0 0 0 0 00 Measured properties n_(d) 2.0012 d_(RT) g/cm³ 3.786 3.458 3.477n_(632.8 nm) 1.9902 n_(531.9 nm) 2.0201 n_(F) 2.0426 T_(liq) ° C. 1175.01135.0 1165.0 ν_(d) 17.5 (n_(d) − 1)/d_(RT) 0.26445 E GPa 93.427 92.73892.462 92.876 92.945 0.25100 0.25100 0.25000 0.25100 0.24900 Predictedand calculated properties P_(n) [for n_(d)] 1.987 1.885 1.888 1.8871.887 1.886 1.916 1.917 P_(d) [for d_(RT)] g/cm³ 3.797 3.586 3.493 3.4843.477 3.384 3.457 3.455 P_(ν) [for ν_(d)] 17.82 20.30 19.76 19.72 19.6319.67 19.01 19.07 n_(d) − (1.54 + 0.1 * d_(RT)) 0.0668 −0.0132 −0.0011−0.0018 −6.800E−04 0.0078 0.0301 0.0317 n_(d) − (1.58 + 0.1 * d_(RT))0.0268 −0.0532 −0.0411 −0.0418 −0.0407 −0.0322 −0.0099 −0.0083 ν_(d) −(64.5 − 23.4 * n_(d)) −0.1981 −0.0786 −0.5577 −0.6333 −0.7159 −0.6983−0.6619 −0.5643 ν_(d) − (63.7 − 23.4 * n_(d)) 0.6019 0.7214 0.24230.1667 0.0841 0.1018 0.1381 0.2357 Exemplary Glass 65 66 67 68 69 70 7172 Composition - mol. % P₂O₅ mol. % 24.99 24.49 24.74 24.99 24.99 24.9824.99 24.99 Nb₂O₅ mol. % 24.39 22.39 21.90 21.49 21.99 22.49 21.99 21.99TiO₂ mol. % 21.99 25.99 26.00 25.79 26.39 26.99 26.39 26.40 BaO mol. % 00 2.00 4.30 3.80 3.30 1.80 0 Na₂O mol. % 0.0224 0.0218 0.0219 0.02240.0225 0 0 0 K₂O mol. % 13.30 13.80 12.80 16.59 16.00 15.40 15.99 15.99CaO mol. % 13.29 11.30 10.51 4.80 4.79 4.81 6.81 8.61 Ta₂O₅ mol. % 0.0220.0214 0.0215 0.0189 0.0189 0.0221 0.0218 0.0215 Li₂O mol. % 1.99 1.992.00 2.00 2.00 2.01 2.02 2.00 Measured properties d_(RT) g/cm³ 3.4793.451 3.494 3.487 3.491 3.493 3.453 3.419 T_(liq) ° C. 1090.0 1120.01145.0 1095.0 1100.0 1110.0 E GPa 94.048 95.013 95.496 μ 0.25000 0.247000.24400 Predicted and calculated properties P_(n) [for n_(d)] 1.9101.912 1.911 1.896 1.904 1.912 1.904 1.903 P_(d) [for d_(RT)] g/cm³ 3.4703.459 3.503 3.495 3.498 3.501 3.457 3.420 P_(ν) [for ν_(d)] 19.56 19.2219.36 19.50 19.24 18.99 19.26 19.27 n_(d) − (1.54 + 0.1 * d_(RT)) 0.02310.0264 0.0202 0.0066 0.0143 0.0221 0.0180 0.0214 n_(d) − (1.58 + 0.1 *d_(RT)) −0.0169 −0.0136 −0.0198 −0.0334 −0.0257 −0.0179 −0.0220 −0.0186ν_(d) − (64.5 − 23.4 * n_(d)) −0.2395 −0.5276 −0.4374 −0.6336 −0.7030−0.7639 −0.6926 −0.6864 ν_(d) − (63.7 − 23.4 * n_(d)) 0.5605 0.27240.3626 0.1664 0.0970 0.0361 0.1074 0.1136 Exemplary Glass 73 74 75 76 7778 79 80 Composition - mol. % P₂O₅ mol. % 22.47 19.98 22.48 24.99 24.9924.99 24.73 24.75 Nb₂O₅ mol. % 19.98 19.98 18.48 21.00 20.99 20.29 21.7621.78 TiO₂ mol. % 23.98 23.98 25.89 25.20 25.19 24.41 26.14 26.13 BaOmol. % 7.70 7.69 7.60 4.80 3.80 3.80 3.76 3.76 Na₂O mol. % 0.022 0.04340.0215 0 0.022 0.0216 0.33 0 K₂O mol. % 15.74 16.98 15.54 17.20 13.4010.99 15.51 15.84 CaO mol. % 9.04 10.30 8.95 4.81 10.59 14.49 4.76 4.74Al₂O₃ mol. % 0.0134 0.0132 0.0131 0 0 0 0 0 Ta₂O₅ mol. % 0.0185 0.01830.0181 0 0.0185 0.0181 0.0188 0.0188 MgO mol. % 0.0338 0.0334 0.0331 0 00 0 0 Li₂O mol. % 1.00 0.99 0.98 1.99 1.00 0.98 1.99 1.99 SiO₂ mol. % 00 0 0 0 0 0.99 0.99 Composition constraints SiO₂ + GeO₂ mol. % 0 0 0 0 00 0.9902 0.9913 Measured properties d_(RT) g/cm³ 3.563 3.599 3.546 3.4953.510 3.481 3.475 T_(liq) ° C. 1125.0 Predicted and calculatedproperties P_(n) [for n_(d)] 1.890 1.896 1.887 1.888 1.899 1.896 1.9011.900 P_(d) [for d_(RT)] g/cm³ 3.613 3.646 3.602 3.492 3.525 3.546 3.4923.490 P_(ν) [for ν_(d)] 20.11 19.92 20.11 19.76 19.78 20.16 19.34 19.34n_(d) − (1.54 + 0.1 * d_(RT)) −0.0117 −0.0088 −0.0135 −9.100E−04 0.00620.0015 0.0113 0.0112 n_(d) − (1.58 + 0.1 * d_(RT)) −0.0517 −0.0488−0.0535 −0.0409 −0.0338 −0.0385 −0.0287 −0.0288 ν_(d) − (64.5 − 23.4 *n_(d)) −0.1740 −0.2195 −0.2391 −0.5580 −0.2940 0.0302 −0.6872 −0.6943ν_(d) − (63.7 − 23.4 * n_(d)) 0.6260 0.5805 0.5609 0.2420 0.5060 0.83020.1128 0.1057 Exemplary Glass 81 82 83 84 85 86 87 88 Composition - mol.% P₂O₅ mol. % 24.95 24.97 24.97 24.97 24.97 23.99 24.00 23.99 Nb₂O₅ mol.% 10.21 20.22 12.32 24.45 20.26 28.00 28.00 27.99 TiO₂ mol. % 40.1526.02 34.31 23.64 33.06 21.99 21.98 21.99 BaO mol. % 0 0 0 0 0 12.9614.44 3.02 Na₂O mol. % 0.17 0.10 0.11 0.11 0.13 0 0 0 K₂O mol. % 14.989.51 9.67 10.24 12.34 5.11 5.97 6.91 CaO mol. % 9.53 19.17 18.60 16.569.23 7.92 5.57 16.07 Ta₂O₅ mol. % 0.0103 0.0176 0.0104 0.0219 0.0180.0246 0.0249 0.0265 Measured properties n_(d) 1.9547 1.9409 1.9448d_(RT) g/cm³ 3.222 3.537 3.403 3.539 3.443 n_(632.8 nm) 1.9440 1.93201.9388 n_(531.9 nm) 1.9727 1.9557 1.9545 15-min devit test (0/1) 1 1 1 11 1 1 1 Predicted and calculated properties P_(n) [for n_(d)] 1.8751.906 1.880 1.927 1.930 1.968 1.966 1.961 P_(d) [for d_(RT)] g/cm³ 3.3473.493 3.424 3.523 3.468 3.904 3.924 3.678 P_(ν) [for ν_(d)] 19.55 19.8620.27 19.20 18.39 18.46 18.45 18.54 n_(d) − (1.54 + 0.1 * d_(RT))1.200E−04 0.0170 −0.0025 0.0350 0.0430 0.0376 0.0336 0.0534 n_(d) −(1.58 + 0.1 * d_(RT)) −0.0399 −0.0230 −0.0425 −0.0050 0.0030 −0.0024−0.0064 0.0134 ν_(d) − (64.5 − 23.4 * n_(d)) −1.078 −0.0354 −0.2402−0.2005 −0.9483 0.0120 −0.0470 −0.0669 ν_(d) − (63.7 − 23.4 * n_(d))−0.2776 0.7646 0.5598 0.5995 −0.1483 0.8120 0.7530 0.7331 ExemplaryGlass 89 90 91 92 93 94 95 96 Composition - mol. % P₂O₅ mol. % 24.0023.99 23.99 24.00 23.99 23.99 23.99 23.99 Nb₂O₅ mol. % 28.00 32.00 32.0032.00 32.00 31.99 32.00 31.99 TiO₂ mol. % 21.99 17.99 18.00 17.99 18.0018.00 17.98 18.00 BaO mol. % 8.63 11.00 7.70 12.95 9.68 14.45 7.39 11.04K₂O mol. % 8.00 4.00 5.19 5.11 6.15 5.97 6.96 6.95 CaO mol. % 9.36 10.9813.10 7.92 10.15 5.57 11.64 8.01 Ta₂O₅ mol. % 0.0241 0.029 0.0285 0.02950.029 0.0298 0.0286 0.0293 Measured properties n_(d) 1.9479 1.95721.9691 1.9875 1.9532 d_(RT) g/cm³ 3.883 3.903 3.832 3.909 3.786 3.860n_(632.8 nm) 1.9360 1.9480 1.9590 1.9750 1.9440 n_(531.9 nm) 1.96811.9725 1.9861 2.0087 1.9685 (n_(d) − 1)/d_(RT) 0.24829 0.25261 0.2517615-min devit test (0/1) 1 1 1 1 1 1 1 1 Predicted and calculatedproperties P_(n) [for n_(d)] 1.960 1.985 1.981 1.982 1.979 1.980 1.9761.977 P_(d) [for d_(RT)] g/cm³ 3.780 3.911 3.829 3.938 3.858 3.959 3.8013.877 P_(ν) [for ν_(d)] 18.49 18.27 18.29 18.25 18.27 18.24 18.29 18.26n_(d) − (1.54 + 0.1 * d_(RT)) 0.0416 0.0534 0.0578 0.0482 0.0529 0.04420.0559 0.0491 n_(d) − (1.58 + 0.1 * d_(RT)) 0.0016 0.0134 0.0178 0.00820.0129 0.0042 0.0159 0.0091 ν_(d) − (64.5 − 23.4 * n_(d)) −0.1556 0.20620.1421 0.1299 0.0745 0.0709 0.0315 0.0204 ν_(d) − (63.7 − 23.4 * n_(d))0.6444 1.006 0.9421 0.9299 0.8745 0.8709 0.8315 0.8204 Exemplary Glass97 98 99 100 101 102 103 104 Composition - mol. % P₂O₅ mol. % 23.9923.98 23.99 23.89 23.89 23.88 23.89 23.90 Nb₂O₅ mol. % 31.98 31.99 32.0028.01 27.43 29.12 27.00 28.50 TiO₂ mol. % 17.99 17.99 18.00 21.99 22.5820.89 23.03 21.52 BaO mol. % 15.96 8.56 12.51 6.12 6.11 6.11 6.11 6.11K₂O mol. % 6.83 7.99 8.00 3.96 5.12 5.07 5.98 6.08 CaO mol. % 3.20 9.455.48 16.01 14.84 14.91 13.97 13.87 Ta₂O₅ mol. % 0.0301 0.0289 0.02960.0268 0.0267 0.0273 0.0233 0.0271 SrO mol. % 0.0161 0 0 0 0 0 0 0Measured properties n_(d) 1.962 1.9491 1.9751 1.9398 d_(RT) g/cm³ 3.9353.802 3.872 3.766 3.725 3.738 3.706 3.718 n_(632.8 nm) 1.9516 1.93901.9740 1.9300 n_(531.9 nm) 1.9797 1.9661 1.9766 1.9562 (n_(d) −1)/d_(RT) 0.24448 0.24511 0.26176 0.25358 15-min devit test (0/1) 1 1 11 1 1 1 1 Predicted and calculated properties P_(n) [for n_(d)] 1.9781.974 1.975 1.970 1.965 1.971 1.961 1.966 P_(d) [for d_(RT)] g/cm³ 3.9793.813 3.894 3.779 3.760 3.775 3.746 3.757 P_(ν) [for ν_(d)] 18.23 18.2818.25 18.51 18.54 18.45 18.56 18.48 n_(d) − (1.54 + 0.1 * d_(RT)) 0.04010.0523 0.0450 0.0521 0.0490 0.0535 0.0467 0.0505 n_(d) − (1.58 + 0.1 *d_(RT)) 8.400E−05 0.0123 0.0051 0.0121 0.0090 0.0135 0.0067 0.0105 ν_(d)− (64.5 − 23.4 * n_(d)) 0.0137 −0.0375 −0.0515 0.1106 0.0194 0.0720−0.0476 −0.0110 ν_(d) − (63.7 − 23.4 * n_(d)) 0.8137 0.7625 0.74850.9106 0.8194 0.8720 0.7524 0.7890 Exemplary Glass 105 106 107 108 109110 111 112 Composition - mol. % P₂O₅ mol. % 23.90 23.90 23.90 23.9023.90 23.91 23.91 23.90 Nb₂O₅ mol. % 29.98 26.57 28.09 29.27 30.85 26.0227.63 28.91 TiO₂ mol. % 20.03 23.45 21.94 20.74 19.17 24.01 22.38 21.10BaO mol. % 6.11 6.12 6.11 6.11 6.12 6.11 6.11 6.11 K₂O mol. % 5.91 6.836.88 6.87 6.77 7.93 7.94 7.94 CaO mol. % 14.04 13.12 13.05 13.08 13.1712.00 12.01 12.01 Ta₂O₅ mol. % 0.0276 0.0232 0.0271 0.0274 0.028 0.02310.027 0.0274 Measured properties n_(d) 1.9853 1.9707 d_(RT) g/cm³ 3.7543.709 3.698 3.738 3.757 3.687 3.694 3.708 n_(632.8 nm) 1.9740 1.9600n_(531.9 nm) 2.0044 1.9887 (n_(d) − 1)/d_(RT) 0.26246 0.26277 15-mindevit test (0/1) 1 1 1 1 1 1 1 1 Predicted and calculated propertiesP_(n) [for n_(d)] 1.972 1.958 1.963 1.967 1.973 1.953 1.958 1.963 P_(d)[for d_(RT)] g/cm³ 3.772 3.732 3.744 3.754 3.769 3.714 3.728 3.738 P_(ν)[for ν_(d)] 18.40 18.58 18.50 18.44 18.35 18.61 18.52 18.45 n_(d) −(1.54 + 0.1 * d_(RT)) 0.0547 0.0443 0.0483 0.0514 0.0557 0.0413 0.04560.0490 n_(d) − (1.58 + 0.1 * d_(RT)) 0.0147 0.0043 0.0083 0.0114 0.01570.0014 0.0056 0.0090 ν_(d) − (64.5 − 23.4 * n_(d)) 0.0426 −0.1129−0.0746 −0.0384 0.0136 −0.1997 −0.1533 −0.1168 ν_(d) − (63.7 − 23.4 *n_(d)) 0.8426 0.6871 0.7254 0.7616 0.8136 0.6003 0.6467 0.6832 ExemplaryGlass 113 114 115 116 117 118 119 120 Composition - mol. % P₂O₅ mol. %23.90 23.91 23.94 23.98 23.98 23.98 23.98 23.98 Nb₂O₅ mol. % 30.23 32.0231.98 30.98 29.52 30.99 28.43 29.62 TiO₂ mol. % 19.79 18.00 18.98 19.9919.99 18.56 19.99 18.66 BaO mol. % 6.11 6.11 8.00 8.01 8.01 8.01 8.018.01 Na₂O mol. % 0 0 2.28 0 0 0 0 0 K₂O mol. % 7.93 7.94 5.74 8.00 8.007.99 8.00 8.00 CaO mol. % 12.01 11.99 9.07 9.01 9.01 9.01 9.01 9.02Ta₂O₅ mol. % 0.0278 0.0285 0.0287 0.0285 0.029 0.0295 0.0257 0.0262Bi₂O₃ mol. % 0 0 0 0 1.47 1.43 2.56 2.70 Measured properties n_(d)1.9398 1.9657 1.9566 1.9678 d_(RT) g/cm³ 3.718 3.746 3.755 3.862 3.8743.921 3.949 n_(632.8 nm) 1.9300 1.9550 1.9450 1.9580 n_(531.9 nm) 1.95621.9837 1.9762 1.9842 (n_(d) − 1)/d_(RT) 0.25276 0.24768 0.24981 15-mindevit test (0/1) 1 1 1 1 1 1 1 1 Predicted and calculated propertiesP_(n) [for n_(d)] 1.968 1.974 1.980 1.974 1.976 1.981 1.977 1.982 P_(d)[for d_(RT)] g/cm³ 3.750 3.765 3.815 3.794 3.871 3.882 3.928 3.946 P_(ν)[for ν_(d)] 18.38 18.29 18.11 18.15 18.26 18.18 18.34 18.28 n_(d) −(1.54 + 0.1 * d_(RT)) 0.0525 0.0573 0.0581 0.0548 0.0488 0.0528 0.04420.0472 n_(d) − (1.58 + 0.1 * d_(RT)) 0.0125 0.0173 0.0181 0.0148 0.00880.0128 0.0042 0.0072 ν_(d) − (64.5 − 23.4 * n_(d)) −0.0785 −0.0262−0.0722 −0.1490 −0.0079 0.0323 0.0972 0.1508 ν_(d) − (63.7 − 23.4 *n_(d)) 0.7215 0.7738 0.7278 0.6510 0.7921 0.8323 0.8972 0.9508 ExemplaryGlass 121 122 123 124 125 126 127 128 Composition - mol. % P₂O₅ mol. %23.97 23.98 23.97 23.97 23.98 24.99 25.00 25.00 Nb₂O₅ mol. % 30.98 27.3628.61 29.62 31.00 19.99 25.00 22.18 TiO₂ mol. % 17.48 19.99 18.67 17.6716.40 24.99 20.00 26.58 BaO mol. % 8.01 8.01 8.01 8.00 8.01 0 0 0 K₂Omol. % 8.00 8.00 8.01 8.00 8.00 14.00 14.01 13.81 CaO mol. % 9.03 9.019.01 9.01 9.01 15.00 14.99 11.43 Ta₂O₅ mol. % 0.0302 0.0261 0.02650.0268 0.0271 0.0177 0.0222 0.0215 Li₂O mol. % 0 0 0 0 0 1.01 0.98 1.00Bi₂O₃ mol. % 2.51 3.62 3.70 3.69 3.58 0 0 0 Measured properties n_(d)1.969 1.8736 1.8915 d_(RT) g/cm³ 3.945 3.996 4.023 4.020 4.025 3.418n_(632.8 nm) 1.9580 1.8661 1.8834 n_(531.9 nm) 1.9876 1.8861 1.9050(n_(d) − 1)/d_(RT) 0.24249 15-min devit test (0/1) 1 1 1 1 1 1 1Predicted and calculated properties P_(n) [for n_(d)] 1.986 1.978 1.9831.986 1.991 1.888 1.905 1.912 P_(d) [for d_(RT)] g/cm³ 3.947 3.983 3.9994.007 4.012 3.429 3.472 3.455 P_(ν) [for ν_(d)] 18.20 18.41 18.35 18.2918.22 20.15 19.83 19.19 n_(d) − (1.54 + 0.1 * d_(RT)) 0.0511 0.03980.0431 0.0458 0.0496 0.0048 0.0181 0.0267 n_(d) − (1.58 + 0.1 * d_(RT))0.0111 −1.800E−04 0.0031 0.0058 0.0096 −0.0352 −0.0219 −0.0133 ν_(d) −(64.5 − 23.4 * n_(d)) 0.1688 0.2010 0.2467 0.2759 0.3041 −0.1834 −0.0912−0.5644 ν_(d) − (63.7 − 23.4 * n_(d)) 0.9688 1.001 1.047 1.076 1.1040.6166 0.7088 0.2356 Exemplary Glass 129 130 131 132 133 134 135 136Composition - mol. % P₂O₅ mol. % 25.00 24.98 24.99 24.98 25.00 24.9824.99 24.98 Nb₂O₅ mol. % 20.45 20.77 21.82 21.99 21.35 20.70 20.90 20.20TiO₂ mol. % 24.50 24.89 26.15 25.98 25.33 24.51 24.90 24.05 BaO mol. % 01.58 3.49 3.00 2.02 4.71 1.36 3.54 Na₂O mol. % 0 0 0 0 0.0217 0 0.02140.0214 K₂O mol. % 9.43 10.27 12.94 12.99 12.03 9.83 11.36 9.24 CaO mol.% 19.61 16.47 9.55 10.00 13.24 14.22 15.46 16.91 Ta₂O₅ mol. % 0.01760.018 0.0187 0.0218 0.0183 0.0183 0.018 0.018 SrO mol. % 0 0.0128 0.02660.0265 0.013 0.0391 0.0128 0.0256 Li₂O mol. % 1.00 1.02 1.01 1.01 0.990.99 0.98 1.02 Measured properties d_(RT) g/cm³ 3.444 3.473 3.497 3.4873.486 3.529 3.464 3.519 Predicted and calculated properties P_(n) [forn_(d)] 1.901 1.903 1.911 1.911 1.905 1.903 1.902 1.898 P_(d) [ford_(RT)] g/cm³ 3.488 3.514 3.534 3.524 3.508 3.584 3.498 3.561 P_(ν) [forν_(d)] 20.14 19.94 19.35 19.34 19.67 20.02 19.90 20.28 n_(d) − (1.54 +0.1 * d_(RT)) 0.0121 0.0119 0.0172 0.0184 0.0144 0.0046 0.0117 0.0023n_(d) − (1.58 + 0.1 * d_(RT)) −0.0279 −0.0281 −0.0228 −0.0216 −0.0256−0.0354 −0.0283 −0.0377 ν_(d) − (64.5 − 23.4 * n_(d)) 0.1220 −0.0225−0.4474 −0.4441 −0.2482 0.0457 −0.1063 0.2013 ν_(d) − (63.7 − 23.4 *n_(d)) 0.9220 0.7775 0.3526 0.3559 0.5518 0.8457 0.6937 1.001 ExemplaryGlass 137 138 139 140 141 142 143 144 Composition - mol. % P₂O₅ mol. %24.98 25.00 24.99 24.99 25.00 25.00 25.01 25.00 Nb₂O₅ mol. % 20.48 19.9919.98 20.79 18.27 16.64 19.12 16.81 TiO₂ mol. % 24.48 23.98 27.98 27.9928.00 27.99 28.00 27.99 BaO mol. % 0.74 0 0 0 0 0 0 0 Na₂O mol. % 0.04230.0416 0 0 0 0 0 0 K₂O mol. % 10.73 10.00 13.99 12.70 11.20 10.64 10.188.96 CaO mol. % 17.51 19.98 8.02 12.49 12.86 12.04 16.69 16.63 Ta₂O₅mol. % 0.0178 0.0175 0.0188 0.018 0.0181 0.0152 0.0174 0.0146 Li₂O mol.% 1.01 0.99 1.02 1.02 0.98 0.99 0.99 0.99 WO₃ mol. % 0 0 4.00 0 3.676.69 0 3.60 Measured properties d_(RT) g/cm³ 3.444 3.428 3.515 3.4133.501 3.560 3.410 3.491 Predicted and calculated properties P_(n) [forn_(d)] 1.898 1.894 1.914 1.910 1.907 1.906 1.904 1.901 P_(d) [ford_(RT)] g/cm³ 3.488 3.476 3.554 3.457 3.561 3.643 3.470 3.571 P_(ν) [forν_(d)] 20.12 20.40 18.92 19.27 19.43 19.44 19.73 19.85 n_(d) − (1.54 +0.1 * d_(RT)) 0.0091 0.0060 0.0191 0.0247 0.0111 0.0020 0.0167 0.0041n_(d) − (1.58 + 0.1 * d_(RT)) −0.0309 −0.0340 −0.0209 −0.0153 −0.0289−0.0380 −0.0233 −0.0359 ν_(d) − (64.5 − 23.4 * n_(d)) 0.0318 0.2041−0.7807 −0.5300 −0.4470 −0.4578 −0.2191 −0.1594 ν_(d) − (63.7 − 23.4 *n_(d)) 0.8318 1.004 0.0193 0.2700 0.3530 0.3422 0.5809 0.6406 ExemplaryGlass 145 146 Composition - mol. % P₂O₅ mol. % 25.00 24.99 Nb₂O₅ mol. %15.26 13.60 TiO₂ mol. % 27.98 27.99 K₂O mol. % 8.25 7.60 CaO mol. %16.34 15.68 Ta₂O₅ mol. % 0.0147 0.0119 Li₂O mol. % 1.00 1.01 WO₃ mol. %6.15 9.12 Measured properties d_(RT) g/cm³ 3.560 3.616 Predicted andcalculated properties P_(n) [for n_(d)] 1.900 1.899 P_(d) [for d_(RT)]g/cm³ 3.642 3.723 P_(ν) [for ν_(d)] 19.91 19.94 n_(d) − (1.54 + 0.1 *d_(RT)) −0.0044 −0.0136 n_(d) − (1.58 + 0.1 * d_(RT)) −0.0444 −0.0536ν_(d) − (64.5 − 23.4 * n_(d)) −0.1365 −0.1353 ν_(d) − (63.7 − 23.4 *n_(d)) 0.6635 0.6647

Table 6 below lists the glass compositions and properties forComparative Glasses 1-22.

TABLE 6 Compositions and Properties of Comparative Example GlassesComparative Examples C1 C2 C3 C4 C5 C6 C7 C8 Reference [14]  [5] [9] [2][6] [3] [7] [4] Composition - mol. % P₂O₅ mol. %   34.70   39.90   27.32  20.66   20.63   24.99   20.65   22.89 Na₂O mol. %   28.10   0.83  5.39   6.07   6.07   3.40   7.28   35.16 K₂O mol. %   12.30   0.55  13.92   7.18   7.17   3.30   6.39   5.86 TiO₂ mol. %   13.50   1.29  14.74   16.00   15.98   20.01   15.06   10.73 Al₂O₃ mol. %   5.70 0 00 0 0 0 0 ZnO mol. %   3.30 0 0 0 0 0 0 0 CaO mol. %   1.20   6.12  13.68   2.68   2.68   8.01   2.68   4.30 MgO mol. %   1.20   1.28 0 00 0 0 0 PbO mol. % 0   46.90 0 0 0 0 0 0 Nb₂O₅ mol. % 0   1.29   24.93  25.74   25.71   21.00   25.74   21.06 Li₂O mol. % 0   1.72 0 0 0  3.29 0 0 Sb₂O₃ mol. % 0   0.12    0.0145 0   0.10 0    0.0258   0.0087 BaO mol. % 0 0 0   15.20   15.18   8.00   15.69 0 B₂O₃ mol. %0 0 0   6.48   6.46 0   6.48 0 SrO mol. % 0 0 0 0 0   8.00 0 0 Ta₂O₅mol. % 0 0 0 0 0    0.0188 0 0 Measured properties n_(d)    1.5711   1.792    1.8504    1.9186    1.9186    1.9186    1.780 n_(632.8 nm)   1.5682    1.8425    1.9098    1.9098    1.9098    1.7737 n_(531.9 nm)   1.5762    1.8635    1.9334    1.9334    1.9335    1.7905 n_(F)   1.5818    1.8790    1.9507    1.9507    1.9509    1.8027 T_(g) ° C. 681.00 T_(x) ° C.  856.00 T_(x) − T_(g) ° C.  175.00 T_(liq) ° C.1100.0   ν_(d)  38.2  21.6  20.6  20.6  20.5  24.6 P_(g−F)     0.63630Predicted properties P_(n) [for n_(d)]    1.583    1.820    1.865   1.904    1.904    1.900    1.900    1.800 P_(d) [for d_(RT)]    2.809   4.964    3.389    3.831    3.831    3.810    3.841    3.321Comparative Examples C9 C10 C11 C12 C13 C14 C15 C16 Reference [8] [1][15]  [10]  [3] [3] [3] [16]  Composition - mol. % P₂O₅ mol. %   16.24  16.19   39.55   27.05   24.99   25.00   25.00   39.55 Na₂O mol. % 0  21.32   32.73   24.51 0   3.39   7.97   32.73 K₂O mol. %   2.82   3.93  6.82   6.61   5.01   3.31   7.00   6.82 TiO₂ mol. %   3.33   9.92  11.36   18.14   22.00   9.99   10.01   11.37 Al₂O₃ mol. % 0 0 0   1.190 0 0 0 ZnO mol. %   3.27 0 0   0.59 0 0   7.99 0 CaO mol. %   1.58  7.07 0   15.01   1.00   9.99   8.00 0 Nb₂O₅ mol. %   21.35   6.26 0  3.46   21.99   26.01   26.00 0 Li₂O mol. %   2.97 0 0 0 0   3.29 0 0BaO mol. %   18.50   5.17 0 0   24.99   9.50   8.00 0 B₂O₃ mol. % 0  4.74 0   3.09 0 0 0 0 SrO mol. %   10.27 0 0 0 0   9.50 0 0 Ta₂O₅ mol.% 0 0 0 0    0.007    0.0236    0.0234 0 WO₃ mol. %   9.18   20.34 0 0 00 0 0 Bi₂O₃ mol. %   4.19 0 0 0 0 0 0 0 GeO₂ mol. %   4.24   5.05 0 0 00 0 0 Cs₂O mol. %   0.63 0 0 0 0 0 0 0 ZrO₂ mol. %   1.44 0 0 0 0 0 0 0CaCl₂ mol. % 0 0   9.09 0 0 0 0   9.09 Sm₂O₃ mol. % 0 0   0.45 0 0 0 0 0SiO₂ mol. % 0 0 0   0.34    0.0258 0 0 0 Nd₂O₃ mol. % 0 0 0 0 0 0 0  0.46 Measured properties n_(d)    1.9694    1.7991    1.580    1.6634   1.583 d_(RT) g/cm³    4.490    2.806    2.900    2.810 n_(632.8 nm)   1.7926    1.6590 n_(531.9 nm)    2.0648    1.8099    1.6705 n_(F)   2.2105    1.8224    1.6787 T_(g) ° C.  416.00  515.00 T_(liq) ° C. 750.00 ν_(d)  21.3  24.6  31.3 P_(g−F)     0.61100 (n_(d) − 1)/d_(RT)    0.21590     0.20670     0.22876     0.20747 α₂₀₋₃₀₀ × 10⁷ K·¹ 105.00 Predicted properties P_(n) [for n_(d)]    1.945    1.790   1.617    1.684    1.920    1.897    1.879    1.617 P_(d) [for d_(RT)]   4.826    4.081    2.969    3.087    4.074    3.900    3.739    2.969Comparative Examples C17 C18 C19 C20 C21 C22 Reference [11]  [3] [3][12]  [2] [13]  Composition - mol. % P₂O₅ mol. %   18.21   24.84   25.00  23.76   20.66   24.12 Na₂O mol. %   13.36   4.99   4.98   11.29   7.280 K₂O mol. %   8.21   5.00   5.01   3.92   6.39   7.60 TiO₂ mol. %  9.95   11.24   15.01   15.46   15.06   10.76 ZnO mol. % 0   4.99 0 0 00 CaO mol. %   5.91   4.14   7.00   4.09   2.68   12.77 Nb₂O₅ mol. %  16.12   35.73   32.01   14.75   25.75   25.38 Li₂O mol. %   11.09  5.02   4.98   17.04 0   4.79 Sb₂O₃ mol. % 0 0 0    0.0437 0 0 BaO mol.% 0   3.99   6.00 0   15.70   8.41 B₂O₃ mol. %   8.88 0 0 0   6.48  6.17 Ta₂O₅ mol. % 0    0.0109    0.0281 0 0 0 WO₃ mol. % 0    0.007 0  9.06 0 0 Bi₂O₃ mol. % 0 0 0   0.60 0 0 SiO₂ mol. %   8.27    0.0268 00 0 0 Fe₂O₃ mol. % 0    0.0303 0 0 0 0 Measured properties n_(d)   1.7582    1.8559    1.9186    1.9005 n_(632.8 nm)    1.7526    1.8482   1.9098    1.8921 n_(531.9 nm)    1.7675    1.8689    1.9335    1.9146n_(F)    1.7782    1.8840    1.9509    1.9311 T_(g) ° C.  493.00 T_(liq)° C.  900.00 1140.0   ν_(d) 27.1  21.9  20.5  21.2 Predicted propertiesP_(n) [for n_(d)]    1.756    1.965    1.951    1.838    1.900    1.871P_(d) [for d_(RT)]    3.200    3.741    3.705    3.636    3.841    3.623

The reference key for each of the Comparative Glasses listed in Table 6is as follows: [1] JP2005008518A (HOYA CORP); [2] JP2010083701A (HOYACORP.); [3] US2019063958A1 (CORNING); [4] US2020131076A1 (OHARA K.K.);[5] US6156684A (HOYA CORP); [6] US7531474B2 (HOYA CORPORATION); [7]US7603876B2 (HOYA CORPORATION); [8] U.S. Pat. No. 7,638,448B2 (SCHOTTAG); [9] WO2011086855A1 (OHARA KK); [10] WO2020110341 (HIKARI GLASS CO.,LTD); [11] JPH08157231A (HOYA CORP.); [12] U.S. Pat. No. 7,892,998B2(KONICA MINOLTA ADVANCED LAYERS INC); [13] JPH08104537A (HOYA CORP.);[14] Jahn W., Untersuchungen uber die Violettfarbung titanhaltigerPhosphatglaser., Glastech. Ber., 1966, vol. 39, No. 3, p. 118-126; [15]Moorthy D. V. R., Jayasimhadri M., Jang K., Kumar J. S., Babu A. M.,Moorthy L. R., Spectroscopic characteristics of Sm3+ doped alkalineearth potassium titanium phosphate glasses, Indian J. Engin. Mater.Sci., 2009, vol. 16, No. 3, p. 193-196; [16] Murthy D. V. R., SasikalaT., Jamalaiah B. C., Babu A. M., Kumar J. S., Jayasimhadri M., MoorthyL. R., Investigation on luminescence properties of Nd³⁺ ions inalkaline-earth titanium phosphate glasses, Optics Communications, 2011,vol. 284, No. 2, p. 603-607.

FIG. 6 is a plot showing the relationship between the density parameterP_(d) and the refractive index parameter P_(n) for some of the ExemplaryGlasses and some of the Comparative Glasses. The Exemplary Glasses(filled circles) are the Examples 2, 4 to 7, 9 to 17, 20 to 36, 38 to57, 62 to 72, 77 to 80, 82 and 84 to 144 from Table 5. The ComparativeGlasses (open circles) are the Examples C1 to C10 from Table 6. Thedensity parameter P_(d) that predicts density d_(RT) was determinedaccording to Formula (II). The refractive index parameter P_(n) thatpredicts refractive index n_(d) was determined according to Formula (I).All of the Exemplary Glasses and Comparative Glasses shown in FIG. 6have the features specified in Table 7. In Table 7, the specification“Not limited” refers to a limitation that was not considered whenselecting the compositions. In FIG. 6, some of the above-enumeratedcompositions may be labeled for better visibility, some others may not,and some more glasses may not be shown, which does not affect thefurther conclusions.

TABLE 7 Limitations for glass compositions shown in FIGS. 6 and 7Quantity Unit Min Max P₂O₅ mol. % 10 40 TiO₂ mol. % 0.5 50 K₂O mol. %0.5 35 CaO mol. % 0.5 35 Nb₂O₅ mol. % 0 50 MgO mol. % 0 15 Al₂O₃ mol. %0 10 Li₂O mol. % 0 4.5 V₂O₅ mol. % 0 1 RO mol. % 4 Not limited TeO₂ +SnO₂ + SnO mol. % 0 20 SiO₂ + GeO₂ mol. % 0 15

The above-enumerated Comparative Glasses were selected as having thehighest refractive index parameter P_(n) at comparable values of densityparameter P_(d) among the known glasses that have the features specifiedin Table 7.

The line corresponding to the formula y=1.54+0.1*x shown in FIG. 6provides a visual representation of the differences between theComparative Glasses having the features specified in Table 7 and theExemplary Glasses 2, 4 to 7, 9 to 17, 20 to 36, 38 to 57, 62 to 72, 77to 80, 82 and 84 to 144 according to the present disclosure. As can beseen in FIG. 6, the mentioned Exemplary Glasses (filled circles) andnone of the Comparative Glasses (open circles) represented in FIG. 6fall above the line y=1.54+0.1*x, where y corresponds to the refractiveindex parameter P_(n) and x corresponds to the density parameter P_(d).In other words, some of the Exemplary Glasses and none of theComparative Glasses represented in FIG. 6 satisfy the following formula(V)(a):

P _(n)−(1.54+0.1*P _(d))>0.00  (V)(a)

As can also be seen in FIG. 6, some of Exemplary Glasses and none of theComparative Glasses represented in FIG. 6 fall above the liney=1.58+0.1*x, where y corresponds to the refractive index parameterP_(n) and x corresponds to the density parameter P_(d). In other words,some of the Exemplary Glasses and none of the Comparative Glassesrepresented in FIG. 6 satisfy the following formula (V)(b):

P _(n)−(1.58+0.1*P _(d))>0.00  (V)(b)

This means that, under the conditions specified in Table 7 above, someof the Exemplary Glasses have higher values of P_(n) at comparablevalues of P_(d) than the best of the Comparative Glasses satisfying thesame conditions. In other words, these Exemplary Glasses, by prediction,have higher values of the refractive index n_(d) at comparable values ofdensity d_(RT) among the glasses, i.e. they are, by prediction, superiorin terms of the combination of d_(RT) and n_(d) to the best knownComparative Glasses that have the features specified in Table 7.

FIG. 7 is a plot showing the relationship between the density d_(RT) andthe refractive index n_(d) for some of the Exemplary Glasses and some ofthe Comparative Glasses. The Exemplary Glasses (filled circles) are theExamples 4 to 7, 9, 10, 26, 28, 30 to 36, 42 to 48, 53, 55, 57, 92, 94,95, 97, 99, 101, 103, 105, 111, 113, 117, 118 and 122 from Table 5. TheComparative Glasses (open circles) are the Examples C6, C9 and C11 toC16 from Table 6. All of the Exemplary Glasses and Comparative Glassesshown in FIG. 7 have the features specified in Table 7. In FIG. 7, someof the above-enumerated compositions may be labeled for bettervisibility, some others may not, and some more glasses may not be shown,which does not affect the further conclusions.

The above-enumerated Comparative Glasses for FIG. 7 were selected ashaving the highest measured values of the refractive index n_(d) atcomparable values of the density d_(RT) among the known glasses thathave the features specified in Table 7.

The line corresponding to the formula y=1.54+0.1*x shown in FIG. 7provides a visual representation of the differences between theComparative Glasses having the features specified in Table 7 and theExemplary Glasses 4 to 7, 9, 10, 26, 28, 30 to 36, 42 to 48, 53, 55, 57,92, 94, 95, 97, 99, 101, 103, 105, 111, 113, 117, 118 and 122 accordingto the present disclosure. As can be seen in FIG. 7, the mentionedExemplary Glasses (filled circles) and none of the Comparative Glasses(open circles) represented in FIG. 7 fall above the line y=1.54+0.1*x,where y corresponds to n_(d) and x corresponds to d_(RT). In otherwords, some of the Exemplary Glasses and none of the Comparative Glassesrepresented in FIG. 7 satisfy the following formula (VI)(a):

n _(d)−(1.54+0.1*d _(RT))>0.00  (VI)(a)

As can also be seen in FIG. 7, some of Exemplary Glasses and none of theComparative Glasses represented in FIG. 7 fall above the liney=1.58+0.1*x, where y corresponds to n_(d) and x corresponds to d_(RT).In other words, some of the Exemplary Glasses and none of theComparative Glasses represented in FIG. 7 satisfy the following formula(VI)(b):

n _(d)−(1.58+0.1*d _(RT))>0.00  (VI)(b)

This means that, under the conditions specified in Table 7 above, someof the Exemplary Glasses have higher measured values of the refractiveindex n_(d) at comparable measured values of the density d_(RT) than thebest of the Comparative Glasses satisfying the same conditions. This canbe interpreted as these Exemplary Glasses, according to measurements,have higher values of n_(d) at comparable values of d_(RT) among theglasses, i.e. they are, according to measurement, superior in terms ofthe combination of d_(RT) and n_(d) to the best known ComparativeGlasses that have the features specified in Table 7.

The values of all attributes specified in Table 7 and Formulas (V)(a),(V)(b), (VI)(a) and (VI)(b) for the Comparative Glasses C1 to C16plotted in FIGS. 6 and 7 are presented in Table 8 below. Fullcompositions of Comparative Glasses are presented in Table 6. Fullcompositions and above-mentioned attributes of the Exemplary Glassesfrom the present disclosure are presented in Table 5.

TABLE 8 Attributes of Comparative Example Glasses Having the Features ofTable 7 Ex. # C1 C2 C3 C4 C5 C6 C7 C8 Composition RO mol. % 5.70 54.3013.67 17.88 17.86 24.02 18.37 4.30 TiO₂ mol. % 13.50 1.29 14.74 16.0015.98 19.99 15.06 10.72 K₂O mol. % 12.30 0.55 13.92 7.18 7.18 3.30 6.395.87 CaO mol. % 1.20 6.12 13.67 2.68 2.68 8.02 2.68 4.30 Nb₂O₅ mol. % 01.29 24.94 25.74 25.71 20.99 25.74 21.05 MgO mol. % 1.20 1.28 0 0 0 0 00 Al₂O₃ mol. % 5.70 0 0 0 0 0 0 0 Li₂O mol. % 0 1.72 0 0 0 3.28 0 0 V₂O₅mol. % 0 0 0 0 0 0 0 0 TeO₂ + SnO₂ + SnO mol. % 0 0 0 0 0 0 0 0 SiO₂ +GeO₂ mol. % 0 0 0 0 0 0 0 0 Measured properties d_(RT) g/cm³ 3.759 n_(d)1.5711 1.792 1.8504 1.9186 1.9186 1.909 1.9186 1.780 n_(d) − (1.54 +0.1 * d_(RT)) −0.0069 n_(d) − (1.58 + 0.1 * d_(RT)) −0.0469 Predictedproperties P_(d) g/cm³ 2.8087 4.9638 3.3889 3.8305 3.8307 3.8096 3.84063.3212 P_(n) 1.5828 1.8204 1.8645 1.9043 1.9042 1.8999 1.9002 1.8001P_(n) − (1.54 + 0.1 * P_(d)) −0.2380 −0.2159 −0.0143 −0.0187 −0.0188−0.0211 −0.0238 −0.0720 P_(n) − (1.58 + 0.1 * P_(d)) −0.2780 −0.2559−0.0543 −0.0587 −0.0588 −0.0611 −0.0638 −0.1120 Ex. # C9 C10 C11 C12 C13C14 C15 C16 Composition RO mol. % 33.62 12.24 8.33 15.63 26.04 29.0024.05 8.33 TiO₂ mol. % 3.33 9.92 10.42 18.12 21.97 9.99 9.99 10.42 K₂Omol. % 2.82 3.93 6.25 6.63 5.02 3.31 7.01 6.25 CaO mol. % 1.58 7.07 8.3315.04 1.00 10.00 8.00 8.33 Nb₂O₅ mol. % 21.35 6.26 0 3.46 21.97 26.0025.98 0 MgO mol. % 0 0 0 0 0 0 0 0 Al₂O₃ mol. % 0 0 0 1.19 0 0 0 0 Li₂Omol. % 2.97 0 0 0 0 3.28 0 0 V₂O₅ mol. % 0 0 0 0 0 0 0 0 TeO₂ + SnO₂ +SnO mol. % 0 0 0 0 0 0 0 0 SiO₂ + GeO₂ mol. % 4.24 5.05 0 0.34 0.0258 00 0 Measured properties d_(RT) g/cm³ 4.490 2.806 2.900 3.957 3.857 3.7462.810 n_(d) 1.9694 1.7991 1.580 1.6634 1.9096 1.897 1.885 1.583 n_(d) −(1.54 + 0.1 * d_(RT)) −0.0196 −0.2406 −0.1666 −0.0261 −0.0287 −0.0296−0.238 n_(d) − (1.58 + 0.1 * d_(RT)) −0.0596 −0.2806 −0.2066 −0.0661−0.0687 −0.0696 −0.278 Predicted properties P_(d) g/cm³ 4.8255 4.08062.9692 3.0871 4.0739 3.8995 3.7394 2.9692 P_(n) 1.9447 1.7903 1.61711.6843 1.9198 1.8971 1.8785 1.6171 P_(n) − (1.54 + 0.1 * P_(d)) −0.0778−0.1578 −0.2199 −0.1645 −0.0276 −0.0328 −0.0354 −0.2199 P_(n) − (1.58 +0.1 * P_(d)) −0.1178 −0.1978 −0.2599 −0.2045 −0.0676 −0.0728 −0.0754−0.2599

As follows from FIGS. 6 and 7, both predicted and measured property dataconfirms that some Exemplary Glasses from the present disclosure havebetter combination of density d_(RT) and refractive index n_(d) than thebest of the Comparative Glasses that have the features specified inTable 7.

FIG. 8 is a plot showing the relationship between the refractive indexparameter P_(n) and the dispersion parameter P_(ν) for some of theExemplary Glasses and some of the Comparative Glasses. The ExemplaryGlasses (filled circles) are the Examples 6 to 10, 16 to 21, 26 to 29,33 to 36, 38, 39, 42 to 77, 79 to 85, 87 to 89, 98, 99, 103, 104, 106 to108, 110 to 117, 126 to 128, 130 to 133, 135 and 139 to 146 from Table5. The Comparative Glasses (open circles) are the Examples C3 to C5, C7,C8, C10 and C17 to C20 from Table 6. The refractive index parameterP_(n) that predicts refractive index at 587.56 nm was determinedaccording to Formula (I). The dispersion parameter P_(ν) that predictsAbbe number was determined according to Formula (III) All of theExemplary Glasses and Comparative Glasses shown in FIG. 8 have thefeatures specified in Table 9. In Table 9, the specification “Notlimited” refers to a limitation that was not considered when selectingthe compositions. In FIG. 8, some of the above-enumerated compositionsmay be labeled for better visibility, some others may not, and some moreglasses may not be shown, which does not affect the further conclusions.

TABLE 9 Limitations for glass compositions shown in FIG. 8 Quantity UnitMin Max P₂O₅ mol. % 10 40 TiO₂ mol. % 0.5 50 K₂O mol. % 0.5 35 CaO mol.% 0.5 35 Nb₂O₅ mol. % 0 50 MgO mol. % 0 15 Al₂O₃ mol. % 0 10 V₂O₅ mol. %0  1 RO mol. % 4 Not limited TeO₂ + SnO₂ + SnO mol. % 0 20 SiO₂ + GeO₂mol. % 0 15 P_(n) 1.75 Not limited

The above-enumerated Comparative Glasses were selected as having thelowest dispersion parameter P_(ν) at comparable values of refractiveindex parameter P_(n) among the known glasses that have the featuresspecified in Table 9.

The line corresponding to the formula y=64.5−23.4*x shown in FIG. 8provides a visual representation of the differences between theComparative Glasses having the features specified in Table 9 and theExemplary Glasses 6 to 10, 16 to 21, 26 to 29, 33 to 36, 38, 39, 42 to77, 79 to 85, 87 to 89, 98, 99, 103, 104, 106 to 108, 110 to 117, 126 to128, 130 to 133, 135 and 139 to 146 according to the present disclosure.As can be seen in FIG. 8, the mentioned Exemplary Glasses (filledcircles) and none of the Comparative Glasses (open circles) representedin FIG. 8 fall below the line y=64.5−23.4*x, where y corresponds to thedispersion parameter P_(ν) and x corresponds to the refractive indexparameter P_(n). In other words, some of the Exemplary Glasses and noneof the Comparative Glasses represented in FIG. 8 satisfy the followingformula (VII)(a):

P _(ν)−(64.5−23.4*P _(n))<0  (VII)(a)

As can also be seen in FIG. 8, some of Exemplary Glasses and none of theComparative Glasses represented in FIG. 8 fall below the liney=63.7−23.4*x, where y corresponds to the dispersion parameter P_(ν) andx corresponds to the refractive index parameter P_(n). In other words,some of the Exemplary Glasses and none of the Comparative Glassesrepresented in FIG. 8 satisfy the following formula (VII)(b):

P _(ν)−(63.7−23.4*P _(n))<0  (VII)(b)

This means that, under the conditions specified in Table 9, some of theExemplary Glasses from the present disclosure have lower values of P_(ν)at comparable values of P_(n) than the best of the Comparative Glassessatisfying the same conditions. In other words, these Exemplary Glasses,by prediction, have lower values of the Abbe number ν_(d) at comparablevalues of refractive index n_(d) among the glasses, i.e. they are, byprediction, superior in terms of combination of the n_(d) and ν_(d) tobest known Comparative Glasses that have the features specified in Table9.

FIG. 9 is a plot showing the relationship between the refractive indexn_(d) and the Abbe number ν_(d) for some of the Exemplary Glasses andsome of the Comparative Glasses. The Exemplary Glasses (filled circles)are the Examples 1, 15, 22 to 25, 33 to 35, 47, 48, 55 and 57 from Table5. The Comparative Glasses (open circles) are the Examples C3, C5, C7 toC9, C13, C17 and C20 to C22 from Table 6. All of the Exemplary Glassesand Comparative Glasses shown in FIG. 9 have the features specified inTable 10. In Table 10, the specification “Not limited” refers to alimitation that was not considered when selecting the compositions. InFIG. 9, some of the above-enumerated compositions may be labeled forbetter visibility, some others may not, and some more glasses may not beshown, which does not affect the further conclusions.

TABLE 10 Limitations for glass compositions shown in FIG. 9 QuantityUnit Min Max P₂O₅ mol. % 10 40 TiO₂ mol. % 0.5 50 K₂O mol. % 0.5 35 CaOmol. % 0.5 35 Nb₂O₅ mol. % 0 50 MgO mol. % 0 15 Al₂O₃ mol. % 0 10 V₂O₅mol. % 0  1 RO mol. % 4 Not limited TeO₂ + SnO₂ + SnO mol. % 0 20 SiO₂ +GeO₂ mol. % 0 15 n_(d) 1.75 Not limited

The above-enumerated Comparative Glasses were selected as having thelowest measured values of the Abbe number ν_(d) at comparable values ofthe measured refractive index n_(d) among the known glasses that havethe features specified in Table 10.

The line corresponding to the formula y=64.5−23.4*x shown in FIG. 9provides a visual representation of the differences between theComparative Glasses having the features specified in Table 10 and theExemplary Glasses 1, 15, 22 to 25, 33 to 35, 47, 48, 55 and 57. As canbe seen in FIG. 9, the mentioned Exemplary Glasses (filled circles) andnone of the Comparative Glasses (open circles) represented in FIG. 9fall below the line y=64.5−23.4*x, where y corresponds to ν_(d) and xcorresponds to n_(d). In other words, some of the Exemplary Glasses andnone of the Comparative Glasses represented in FIG. 9 satisfy thefollowing formula (VIII)(a):

ν_(d)−(64.5−23.4*n _(d))<0  (VIII)(a)

As can also be seen in FIG. 9, some of the Exemplary Glasses and none ofthe Comparative Glasses represented in FIG. 9 fall below the liney=63.7−23.4*x, where y corresponds to ν_(d) and x corresponds to n_(d).In other words, some of the Exemplary Glasses and none of theComparative Glasses represented in FIG. 9 satisfy the following formula(VIII)(b):

ν_(d)−(63.7−23.4*n _(d))<  (VIII)(b)

This means that, under the conditions specified in Table 10, some of theExemplary Glasses have lower measured values of the Abbe number ν_(d) atcomparable measured values of the refractive index n_(d) than the bestof the Comparative Glasses satisfying the same conditions. This can beinterpreted as these Exemplary Glasses, according to measurements, havelower values of ν_(d) at comparable values of n_(d) among the glasses,i.e. they are, according to measurement, superior in terms of thecombination of n_(d) and ν_(d) to the best known Comparative Glassesthat have the features specified in Table 10.

The values of all attributes specified in Tables 9 and 10 and Formulas(VII)(a), (VII)(b), (VIII)(a) and (VIII)(b) for the Comparative GlassesC3 to C5, C7 to C10, C13 and C17 to C22 plotted in FIGS. 8 and 9 arepresented in Table 11 below. Full compositions of Comparative Glassesare presented in Table 6. Full compositions and above-mentionedattributes of the Exemplary Glasses are presented in Table 5.

TABLE 11 Attributes of Comparative Example Glasses Having the Featuresof Tables 9 and 10 Ex. # C3 C4 C5 C7 C8 C9 C10 C13 Composition RO mol. %13.67 17.88 17.86 18.37 4.30 33.62 12.24 26.04 TiO₂ mol. % 14.74 16.0015.98 15.06 10.72 3.33 9.92 21.97 K₂O mol. % 13.92 7.18 7.18 6.39 5.872.82 3.93 5.02 CaO mol. % 13.67 2.68 2.68 2.68 4.30 1.58 7.07 1.00 Nb₂O₅mol. % 24.94 25.74 25.71 25.74 21.05 21.35 6.26 21.97 MgO mol. % 0 0 0 00 0 0 0 Al₂O₃ mol. % 0 0 0 0 0 0 0 0 V₂O₅ mol. % 0 0 0 0 0 0 0 0 TeO₂ +SnO₂ + SnO mol. % 0 0 0 0 0 0 0 0 SiO₂ + GeO₂ mol. % 0 0 0 0 0 4.24 5.050.0258 Measured properties n_(d) 1.8504 1.9186 1.9186 1.9186 1.7801.9694 1.7991 1.9096 ν_(d) 21.6 20.6 20.6 20.5 24.6 21.3 24.6 21.2d_(RT) g/cm³ 4.490 3.957 n_(d) − (1.544 + 0.1 * d_(RT)) −0.0236 −0.0301ν_(d) − (64.5 − 23.4 * n_(d)) 0.3994 0.9952 0.9952 0.8952 1.772 2.8842.1589 1.3846 ν_(d) − (63.7 − 23.4 * n_(d)) 1.1994 1.7952 1.7952 1.69522.572 3.684 2.9589 2.1846 Predicted properties P_(n) 1.8645 1.90431.9042 1.9002 1.8001 1.9447 1.7903 1.9198 P_(ν) 21.27 20.35 20.35 20.5623.36 21.74 23.95 20.02 P_(d) g/cm³ 3.3889 3.8305 3.8307 3.8406 3.32124.8255 4.0806 4.0739 P_(n) − (1.544 + 0.1 * P_(d)) −0.0183 −0.0227−0.0228 −0.0278 −0.076 −0.0818 −0.1618 −0.0316 P_(ν) − (64.5 − 23.4 *P_(n)) 0.4016 0.4073 0.4096 0.5276 0.9863 2.7436 1.3426 0.4415 P_(ν) −(63.7 − 23.4 * P_(n)) 1.2016 1.2073 1.2096 1.3276 1.7863 3.5436 2.14261.2415 Ex. # C17 C18 C19 C20 C21 C22 Composition RO mol. % 5.91 13.1613.02 4.09 18.38 21.18 TiO₂ mol. % 9.95 11.22 14.99 15.46 15.06 10.76K₂O mol. % 8.21 5.01 5.02 3.92 6.39 7.60 CaO mol. % 5.91 4.14 7.01 4.092.68 12.77 Nb₂O₅ mol. % 16.12 35.71 32.00 14.75 25.75 25.38 MgO mol. % 00 0 0 0 0 Al₂O₃ mol. % 0 0 0 0 0 0 V₂O₅ mol. % 0 0 0 0 0 0 TeO₂ + SnO₂ +SnO mol. % 0 0 0 0 0 0 SiO₂ + GeO₂ mol. % 8.27 0.0269 0 0 0 0 Measuredproperties n_(d) 1.7582 1.971 1.966 1.8559 1.9186 1.9005 ν_(d) 27.1 21.920.5 21.2 d_(RT) g/cm³ 3.785 3.624 n_(d) − (1.544 + 0.1 * d_(RT)) 0.04850.0596 ν_(d) − (64.5 − 23.4 * n_(d)) 3.7419 0.8281 0.8952 1.1717 ν_(d) −(63.7 − 23.4 * n_(d)) 4.5419 1.6281 1.6952 1.9717 Predicted propertiesP_(n) 1.7563 1.965 1.9505 1.8379 1.9003 1.8707 P_(ν) 26.06 18.79 18.9622.59 20.56 22.20 P_(d) g/cm³ 3.1996 3.7414 3.7054 3.6359 3.8406 3.6232P_(n) − (1.544 + 0.1 * P_(d)) −0.1076 0.0468 0.036 −0.0697 −0.0278−0.0356 P_(ν) − (64.5 − 23.4 * P_(n)) 2.6590 0.2754 0.1042 1.0970 0.52711.4716 P_(ν) − (63.7 − 23.4 * P_(n)) 3.4590 1.0754 0.9042 1.8970 1.32712.2716

As follows from FIGS. 8 and 9, both predicted and measured property dataconfirms that some Exemplary Glasses have better combination of densityd_(RT), refractive index n_(d) and/or Abbe number ν_(d) than the best ofthe Comparative Glasses that have the features specified in Tables 9 and10.

The following non-limiting aspects are encompassed by the presentdisclosure. To the extent not already described, any one of the featuresof the first through the forty-first aspect may be combined in part orin whole with features of any one or more of the other aspects of thepresent disclosure to form additional aspects, even if such acombination is not explicitly described.

According to a first aspect, the glass comprises a plurality ofcomponents, the glass having a composition of the components comprisinggreater than or equal 10.0 mol. % and less than or equal to 40.0 mol. %P₂O₅, greater than or equal to 0.5 mol. % and less than or equal to 50.0mol. % TiO₂, greater than or equal to 0.5 mol. % and less than or equalto 35.0 mol. % K₂O, greater than or equal to 0.5 mol. % and less than orequal to 35.0 mol. % CaO, greater than or equal to 0.0 mol. % and lessthan or equal to 50.0 mol. % Nb₂O₅, greater than or equal to 0.0 mol. %and less than or equal to 15.0 mol. % MgO, greater than or equal to 0.0mol. % and less than or equal to 10.0 mol. % Al₂O₃, greater than orequal to 0.0 mol. % and less than or equal to 4.5 mol. % Li₂O, greaterthan or equal to 0.0 mol. % and less than or equal to 1.0 mol. % V₂O₅,greater than or equal to 4.0 mol. % RO, greater than or equal to 0.0mol. % and less than or equal to 20.0 mol. % for a sum of TeO₂+SnO₂+SnO,greater than or equal to 0.0 mol. % and less than or equal to 15.0 mol.% for a sum of SiO₂+GeO₂ and may optionally contain one or morecomponents selected from Na₂O, WO₃, BaO, SrO, ZnO, PbO, Bi₂O₃, B₂O₃,ZrO₂, Tl₂O, Ag₂O, Cs₂O, Ga₂O₃, La₂O₃, MoO₃ and Ta₂O₅, the glasssatisfying the condition: P_(n)−(1.54+0.1*P_(d))>0.00, where P_(n) is arefractive index parameter calculated from the glass composition interms of mol. % of the components according to the Formula (I):

P_(n)=−0.0043794*P₂O₅+0.0072428*Nb₂O₅+0.0037304*TiO₂−0.00039553*BaO−0.0032012*K₂O−0.00060689*CaO−0.0024218*Na₂O−0.0014988*Li₂O+0.0028587*WO₃+0.0083295*Bi₂O₃−0.0031637*B₂O₃−0.0030702*SiO₂−0.00030248*ZnO+0.0020025*ZrO₂−0.0018173*MgO−0.0032886*Al₂O₃+0.0024221*TeO₂+0.0038137*PbO−0.0016392*GeO₂+0.0063024*Tl₂O+0.0048765*Ag₂O+1.81451,  (I)

P_(d) is a density parameter calculated from the glass composition interms of mol. % of the components according to the Formula (II):

P_(d)[g/cm³]=3.98457−0.015773*Al₂O₃−0.014501*B₂O₃+0.019328*BaO+0.060758*Bi₂O₃−0.0012685*CaO+0.023111*CdO+0.0053184*Cs₂O+0.011488*Ga₂O₃−0.0015416*GeO₂−0.013342*K₂O+0.058319*La₂O₃−0.007918*Li₂O−0.0021423*MgO−0.0024413*MoO₃−0.0082226*Na₂O+0.0084961*Nb₂O₅−0.020501*P₂O₅+0.038898*PbO−0.012720*SiO₂+0.013948*SrO+0.047924*Ta₂O₅+0.011248*TeO₂−0.0092491*V₂O₅+0.028913*WO₃+0.0074702*ZnO+0.0096721*ZrO₂,  (II)

where RO is a total sum of divalent metal oxides, and a symbol “*” meansmultiplication.

According to a second aspect, the glass of the first aspect, wherein theglass satisfies the condition: n_(d)−(1.54+0.1*d_(RT))>0.00, where n_(d)a is refractive index of the glass at 587.56 nm, d_(RT) [g/cm³] is adensity of the glass at room temperature.

According to a third aspect, the glass of any one of aspects 1-2,wherein the glass satisfies the condition: n_(d)−(1.58+0.1*d_(RT))>0.00,where n_(d) is a refractive index of the glass at 587.56 nm, d_(RT)[g/cm³] is a density of the glass at room temperature.

According to a fourth aspect, the glass of any one of aspects 1-3,wherein the glass satisfies the condition: P_(n)−(1.58+0.1*P_(d))>0.00.

According to a fifth aspect, the glass of any one of aspects 1-4,wherein the glass further has predicted properties, calculated fromchemical composition, that satisfy the following criteria satisfies thecondition: P_(d)<4.2 g/cm³.

According to a sixth aspect, the glass of any one of aspects 1-5,wherein the glass has a density at room temperature, d_(RT), less thanor equal to 4.2 g/cm³.

According to a seventh aspect, the glass of the sixth aspect, whereinthe density at room temperature, d_(RT), is less than or equal to 3.8g/cm³.

According to an eighth aspect, the glass of any one of aspects 1-7,wherein the glass satisfies the condition: P_(n)>1.8.

According to a ninth aspect, the glass of any one of aspects 1-8,wherein the glass has a refractive index at 587.56 nm, n_(d), greaterthan or equal to 1.8.

According to a tenth aspect, the glass of the ninth aspect, wherein therefractive index at 587.56 nm, n_(d), is greater than or equal to 1.95.

According to an eleventh aspect, the glass satisfies the condition:P_(ref)>0.24 cm³/g, where P_(ref) is a refraction parameter calculatedfrom the glass composition in terms of mol. % of the componentsaccording to the Formula (IV):

P_(ref)[cm³/g]=0.223637+0.0010703*Nb₂O₅−0.00041688*P₂O₅+0.00088482*TiO₂+0.000054956*CaO−0.00029243*K₂O−0.0008347*BaO−0.00023739*Na₂O+0.000082792*Li₂O−0.0012487*WO₃−0.00042393*ZnO−0.00059152*SrO−0.00018266*MgO−0.0014091*Bi₂O₃−0.0014895*Ta₂O₅−0.00021842*SiO₂−0.00024788*ZrO₂−0.00014801*B₂O₃−0.000060848*TeO₂−0.00085564*PbO−0.00042429*GeO₂−0.0015439*Tl₂O−0.0012936*Ag₂O−0.00089356*Cu₂O−0.00039278*CuO+0.00017895*As₂O₃−0.00011802*Sb₂O₃.  (IV)

According to a twelfth aspect, the glass of any one of aspects 1-11,wherein the glass further has a refraction”), (n_(d)−1)/d_(RT), greaterthan or equal to 0.24 cm³/g.

According to a thirteenth aspect, the glass of the twelfth aspect,wherein the refraction”), (n_(d)−1)/d_(RT), is greater than or equal to0.25 cm³/g.

According to a fourteenth aspect, the glass of any one of aspects 1-13,wherein the composition of the components comprises: greater than orequal to 15.0 mol. % and less than or equal to 35.0 mol. % P₂O₅, greaterthan or equal to 10.0 mol. % and less than or equal to 40.0 mol. %Nb₂O₅, greater than or equal to 0.5 mol. % and less than or equal to40.0 mol. % TiO₂, greater than or equal to 0.5 mol. % and less than orequal to 30.0 mol. % CaO, greater than or equal to 0.5 mol. % and lessthan or equal to 20.0 mol. % K₂O, greater than or equal to 0.0 mol. %and less than or equal to 20.0 mol. % BaO, greater than or equal to 0.0mol. % and less than or equal to 20.0 mol. % Na₂O, greater than or equalto 0.0 mol. % and less than or equal to 10.0 mol. % WO₃, greater than orequal to 0.0 mol. % and less than or equal to 4.0 mol. % Bi₂O₃ andgreater than or equal to 0.0 mol. % and less than or equal to 2.0 mol. %Ta₂O₅.

According to a fifteenth aspect, the glass of any one of aspects 1-14,wherein the composition of the components comprises: greater than orequal to 21.0 mol. % and less than or equal to 30.0 mol. % P₂O₅, greaterthan or equal to 13.0 mol. % and less than or equal to 38.0 mol. %Nb₂O₅, greater than or equal to 9.0 mol. % and less than or equal to37.0 mol. % TiO₂, greater than or equal to 4.0 mol. % and less than orequal to 23.0 mol. % CaO, greater than or equal to 4.0 mol. % and lessthan or equal to 16.0 mol. % K₂O, greater than or equal to 0.0 mol. %and less than or equal to 14.5 mol. % BaO, greater than or equal to 0.0mol. % and less than or equal to 13.5 mol. % Na₂O, greater than or equalto 0.0 mol. % and less than or equal to 8.5 mol. % WO₃, greater than orequal to 0.0 mol. % and less than or equal to 3.4 mol. % Bi₂O₃, greaterthan or equal to 0.0 mol. % and less than or equal to 1.8 mol. % Ta₂O₅and greater than or equal to 0.0 mol. % and less than or equal to 0.9mol. % SiO₂.

According to a sixteenth aspect, the glass of any one of aspects 1-14,wherein the composition of the components comprises: greater than orequal to 22.0 mol. % and less than or equal to 29.0 mol. % P₂O₅, greaterthan or equal to 16.0 mol. % and less than or equal to 35.0 mol. %Nb₂O₅, greater than or equal to 12.0 mol. % and less than or equal to34.0 mol. % TiO₂, greater than or equal to 5.5 mol. % and less than orequal to 20.5 mol. % CaO, greater than or equal to 5.0 mol. % and lessthan or equal to 14.5 mol. % K₂O, greater than or equal to 0.0 mol. %and less than or equal to 13.0 mol. % BaO, greater than or equal to 0.0mol. % and less than or equal to 12.0 mol. % Na₂O, greater than or equalto 0.0 mol. % and less than or equal to 7.5 mol. % WO₃, greater than orequal to 0.0 mol. % and less than or equal to 4.0 mol. % Li₂O, greaterthan or equal to 0.0 mol. % and less than or equal to 3.0 mol. % Bi₂O₃,greater than or equal to 0.0 mol. % and less than or equal to 1.6 mol. %Ta₂O₅ and greater than or equal to 0.0 mol. % and less than or equal to0.8 mol. % SiO₂.

According to a seventeenth aspect, the glass of any one of aspects 1-13,wherein the composition of the components comprises: greater than orequal to 21.7 mol. % and less than or equal to 24.7 mol. % P₂O₅, greaterthan or equal to 21.0 mol. % and less than or equal to 35.0 mol. %Nb₂O₅, greater than or equal to 13.0 mol. % and less than or equal to33.0 mol. % TiO₂, greater than or equal to 6.0 mol. % and less than orequal to 17.0 mol. % BaO, greater than or equal to 2.0 mol. % and lessthan or equal to 13.5 mol. % K₂O, greater than or equal to 0.5 mol. %and less than or equal to 14.5 mol. % CaO, greater than or equal to 0.0mol. % and less than or equal to 10.5 mol. % Na₂O, greater than or equalto 0.0 mol. % and less than or equal to 7.5 mol. % SrO, greater than orequal to 0.0 mol. % and less than or equal to 4.6 mol. % Bi₂O₃, greaterthan or equal to 0.0 mol. % and less than or equal to 4.6 mol. % WO₃,greater than or equal to 0.0 mol. % and less than or equal to 4.6 mol. %ZnO and greater than or equal to 0.0 mol. % and less than or equal to2.5 mol. % MgO.

According to an eighteenth aspect, a glass of any one of aspects 1-17,wherein when cooled in air from 1100° C. to 500° C. in 2.5 minutes, theglass does not crystallize.

According to a nineteenth aspect, a method for manufacturing an opticalelement, the method comprising processing a glass of any one of aspects1-18.

According to a twentieth aspect, an optical element comprising a glassof any one of aspects 1-19.

According to a twenty-first aspect, the glass contains greater than orequal to 10.0 mol. % and less than or equal to 40.0 mol. % P₂O₅, greaterthan or equal to 1.0 mol. % and less than or equal to 50.0 mol. % TiO₂,greater than or equal to 1.0 mol. % and less than or equal to 35.0 mol.% K₂O, greater than or equal to 1.0 mol. % and less than or equal to35.0 mol. % CaO, greater than or equal to 0.0 mol. % and less than orequal to 50.0 mol. % Nb₂O₅, greater than or equal to 0.0 mol. % and lessthan or equal to 15.0 mol. % MgO, greater than or equal to 0.0 mol. %and less than or equal to 10.0 mol. % Al₂O₃, greater than or equal to0.0 mol. % and less than or equal to 1.0 mol. % V₂O₅, greater than orequal to 4.0 mol. % RO, greater than or equal to 0.0 mol. % and lessthan or equal to 20.0 mol. % for a sum of TeO₂+SnO₂+SnO, greater than orequal to 0.0 mol. % and less than or equal to 15.0 mol. % for a sum ofSiO₂+GeO₂ and may optionally contain one or more components selectedfrom Na₂O, Li₂O, WO₃, BaO, SrO, ZnO, PbO, Bi₂O₃, B₂O₃, ZrO₂, Tl₂O, Ag₂O,Ga₂O₃, MoO₃ and Ta₂O₅, wherein the glass satisfies the conditions:P_(n)>1.75 and P_(ν)−(64.5−23.4*P_(n))<0.00, where P_(n) is a refractiveindex parameter calculated from the glass composition in terms of mol. %of the components according to the Formula (I):

P_(n)−−0.0043794*P₂O₅+0.0072428*Nb₂O₅+0.0037304*TiO₂−0.00039553*BaO−0.0032012*K₂O−0.00060689*CaO−0.0024218*Na₂O−0.0014988*Li₂O+0.0028587*WO₃+0.0083295*Bi₂O₃−0.0031637*B₂O₃−0.0030702*SiO₂−0.00030248*ZnO+0.0020025*ZrO₂−0.0018173*MgO−0.0032886*Al₂O₃+0.0024221*TeO₂+0.0038137*PbO−0.0016392*GeO₂+0.0063024*Tl₂O+0.0048765*Ag₂O+1.81451,  (I)

P_(ν) is a dispersion parameter, calculated from the glass compositionin terms of mol. % of the components according to the Formula (III):

P_(ν)=exp(2.11+0.0438*(exp(3.25980+0.0072248*Al₂O₃+0.0055494*B₂O₃+0.0024164*BaO−0.00849*Bi₂O₃+0.0029812*CaO+0.0092768*CdO+0.0099821*Ga₂O₃−0.0038579*GeO₂+0.0028062*K₂O+0.0031951*Li₂O+0.0027011*MgO+0.007976*MoO₃+0.0028705*Na₂O−0.013374*Nb₂O₅+0.0072007*P₂O₅−0.0049796*PbO+0.0032241*SiO₂+0.0050024*SrO−0.002136*Ta₂O₅−0.0032329*TeO₂−0.009788*TiO₂+0.0074782*V₂O₅−0.0057095*WO₃+0.0032826*ZnO+0.009302*ZrO₂))),  (III)

where RO is a total sum of divalent metal oxides and a symbol “*” meansmultiplication.

According to a twenty-second aspect, the glass of the twenty-firstaspect, wherein the glass has a refractive index at 587.56 nm, n_(d),greater than or equal to 1.75, wherein the glass satisfy satisfies theconditions: ν_(d)−(64.5−23.4*n_(d))<0.00 andν_(d)−(63.7−23.4*n_(d))<0.00, where ν_(d) is an Abbe number of theglass.

According to a twenty-third aspect, the glass of any one of aspects21-22, wherein the glass satisfies the condition:ν_(d)−(63.7−23.4*n_(d))<0.00, where ν_(d) is an Abbe number of theglass, and n_(d) is a refractive index of the glass at 587.56 nm.

According to a twenty-fourth aspect, the glass of any one of aspects21-23, wherein the glass satisfies the condition:P_(ν)−(63.7−23.4*P_(n))<0.00.

According to a twenty-fifth aspect, the glass of any one of aspects21-24, wherein the glass satisfies the condition: P_(d)<4.2 g/cm³, whereP_(d) is a density parameter calculated from the glass composition interms of mol. % of the components according to the Formula (II):

P_(d)[g/cm³]=3.98457−0.015773*Al₂O₃−0.014501*B₂O₃+0.019328*BaO+0.060758*Bi₂O₃−0.0012685*CaO+0.023111*CdO+0.0053184*Cs₂O+0.011488*Ga₂O₃−0.0015416*GeO₂−0.013342*K₂O+0.058319*La₂O₃−0.007918*Li₂O−0.0021423*MgO−0.0024413*MoO₃−0.0082226*Na₂O+0.0084961*Nb₂O₅−0.020501*P₂O₅+0.038898*PbO−0.012720*SiO₂+0.013948*SrO+0.047924*Ta₂O₅+0.011248*TeO₂−0.0092491*V₂O₅+0.028913*WO₃+0.0074702*ZnO+0.0096721*ZrO₂.  (II)

According to a twenty-sixth aspect, the glass of any one of aspects21-25, wherein the glass has a density at room temperature, d_(RT), lessthan or equal to 4.2 g/cm³.

According to a twenty-seventh aspect, the density at room temperature,d_(RT) is less than or equal to 3.8 g/cm³.

According to a twenty-eighth aspect, the glass of any one of aspects21-27, wherein the glass satisfies the condition: P_(n)>1.8.

According to a twenty-ninth aspect, the glass of any one of aspects21-28, wherein the glass has a refractive index at 587.56 nm, n_(d)greater than or equal to 1.8.

According to a thirtieth aspect, the glass of the twenty-ninth aspect,wherein the glass has a refractive index at 587.56 nm, n_(d), greaterthan or equal to 1.95.

According to a thirty-first aspect, the glass of any one of aspects21-30, wherein the glass satisfies the condition: P_(ref)>0.24 cm³/g,where P_(ref) is a refraction parameter calculated from the glasscomposition in terms of mol. % of the components according to theFormula (IV):

P_(ref)[cm³/g]=0.223637+0.0010703*Nb₂O₅−0.00041688*P₂O₅+0.00088482*TiO₂+0.000054956*CaO−0.00029243*K₂O−0.0008347*BaO−0.00023739*Na₂O+0.000082792*Li₂O−0.0012487*WO₃−0.00042393*ZnO−0.00059152*SrO−0.00018266*MgO−0.0014091*Bi₂O₃−0.0014895*Ta₂O₅−0.00021842*SiO₂−0.00024788*ZrO₂−0.00014801*B₂O₃−0.000060848*TeO₂−0.00085564*PbO−0.00042429*GeO₂−0.0015439*Tl₂O−0.0012936*Ag₂O−0.00089356*Cu₂O−0.00039278*CuO+0.00017895*As₂O₃−0.00011802*Sb₂O₃.  (IV)

According to a thirty-second aspect, the glass of any one of aspects21-31, wherein the glass has a refraction, (n_(d)−1)/d_(RT), greaterthan or equal to 0.24 cm³/g.

According to a thirty-third aspect, the glass of the thirty-secondaspect, wherein the glass has a refraction, (n_(d)−1)/d_(RT), greaterthan or equal to 0.25 cm³/g.

According to a thirty-fourth aspect, the glass of any one of aspects21-33, wherein the composition of the components comprises: greater thanor equal to 15.0 mol. % and less than or equal to 35.0 mol. % P₂O₅,greater than or equal to 10.0 mol. % and less than or equal to 40.0 mol.% Nb₂O₅, greater than or equal to 1.0 mol. % and less than or equal to40.0 mol. % TiO₂, greater than or equal to 1.0 mol. % and less than orequal to 30.0 mol. % CaO, greater than or equal to 1.0 mol. % and lessthan or equal to 20.0 mol. % K₂O, greater than or equal to 0.0 mol. %and less than or equal to 20.0 mol. % BaO, greater than or equal to 0.0mol. % and less than or equal to 20.0 mol. % Na₂O, greater than or equalto 0.0 mol. % and less than or equal to 10.0 mol. % WO₃, greater than orequal to 0.0 mol. % and less than or equal to 5.0 mol. % Li₂O, greaterthan or equal to 0.0 mol. % and less than or equal to 4.0 mol. % Bi₂O₃and greater than or equal to 0.0 mol. % and less than or equal to 2.0mol. % Ta₂O₅.

According to a thirty-fifth aspect, the glass of any one of aspects21-34, wherein the composition of the components comprises: greater thanor equal to 21.0 mol. % and less than or equal to 30.0 mol. % P₂O₅,greater than or equal to 13.0 mol. % and less than or equal to 38.0 mol.% Nb₂O₅, greater than or equal to 9.0 mol. % and less than or equal to37.0 mol. % TiO₂, greater than or equal to 4.0 mol. % and less than orequal to 23.0 mol. % CaO, greater than or equal to 4.0 mol. % and lessthan or equal to 16.0 mol. % K₂O, greater than or equal to 0.0 mol. %and less than or equal to 14.5 mol. % BaO, greater than or equal to 0.0mol. % and less than or equal to 13.5 mol. % Na₂O, greater than or equalto 0.0 mol. % and less than or equal to 8.5 mol. % WO₃, greater than orequal to 0.0 mol. % and less than or equal to 4.5 mol. % Li₂O, greaterthan or equal to 0.0 mol. % and less than or equal to 3.4 mol. % Bi₂O₃,greater than or equal to 0.0 mol. % and less than or equal to 1.8 mol. %Ta₂O₅ and greater than or equal to 0.0 mol. % and less than or equal to0.9 mol. % SiO₂.

According to a thirty-sixth aspect, the glass of any one of aspects21-35, wherein the composition of the components comprises: greater thanor equal to 22.0 mol. % and less than or equal to 29.0 mol. % P₂O₅,greater than or equal to 16.0 mol. % and less than or equal to 35.0 mol.% Nb₂O₅, greater than or equal to 12.0 mol. % and less than or equal to34.0 mol. % TiO₂, greater than or equal to 5.5 mol. % and less than orequal to 20.5 mol. % CaO, greater than or equal to 5.0 mol. % and lessthan or equal to 14.5 mol. % K₂O, greater than or equal to 0.0 mol. %and less than or equal to 13.0 mol. % BaO, greater than or equal to 0.0mol. % and less than or equal to 12.0 mol. % Na₂O, greater than or equalto 0.0 mol. % and less than or equal to 7.5 mol. % WO₃, greater than orequal to 0.0 mol. % and less than or equal to 4.0 mol. % Li₂O, greaterthan or equal to 0.0 mol. % and less than or equal to 3.0 mol. % Bi₂O₃,greater than or equal to 0.0 mol. % and less than or equal to 1.6 mol. %Ta₂O₅ and greater than or equal to 0.0 mol. % and less than or equal to0.8 mol. % SiO₂.

According to a thirty-seventh aspect, the glass of any one of aspects21-33, wherein the composition of the components comprises: greater thanor equal to 21.7 mol. % and less than or equal to 24.7 mol. % P₂O₅,greater than or equal to 21.0 mol. % and less than or equal to 35.0 mol.% Nb₂O₅, greater than or equal to 13.0 mol. % and less than or equal to33.0 mol. % TiO₂, greater than or equal to 6.0 mol. % and less than orequal to 17.0 mol. % BaO, greater than or equal to 2.0 mol. % and lessthan or equal to 13.5 mol. % K₂O, greater than or equal to 1.0 mol. %and less than or equal to 14.5 mol. % CaO, greater than or equal to 0.0mol. % and less than or equal to 10.5 mol. % Na₂O, greater than or equalto 0.0 mol. % and less than or equal to 7.5 mol. % SrO, greater than orequal to 0.0 mol. % and less than or equal to 6.0 mol. % Li₂O, greaterthan or equal to 0.0 mol. % and less than or equal to 4.6 mol. % Bi₂O₃,greater than or equal to 0.0 mol. % and less than or equal to 4.6 mol. %WO₃, greater than or equal to 0.0 mol. % and less than or equal to 4.6mol. % ZnO and greater than or equal to 0.0 mol. % and less than orequal to 2.5 mol. % MgO.

According to a thirty-eighth aspect, the glass of any one of aspects21-34 and 37, wherein the composition of the components comprises:greater than or equal to 0.0 mol. % and less than or equal to 4.5 mol. %Li₂O.

According to a thirty-ninth aspect, a glass of any one of aspects 21-38,wherein when cooled in air from 1100° C. to 500° C. in 2.5 minutes, theglass does not crystallize.

According to a fortieth aspect, a method for manufacturing an opticalelement, the method comprising processing a glass of any one of aspects21-39.

According to a forty-first aspect, an optical element comprising a glassof any one of aspects 21-40.

Many variations and modifications may be made to the above-describedembodiments of the disclosure without departing substantially from thespirit and various principles of the disclosure. All such modificationsand variations are intended to be included herein within the scope ofthis disclosure and protected by the following claims.

To the extent not already described, the different features of thevarious aspects of the present disclosure may be used in combinationwith each other as desired. That a particular feature is not explicitlyillustrated or described with respect to each aspect of the presentdisclosure is not meant to be construed that it cannot be, but it isdone for the sake of brevity and conciseness of the description. Thus,the various features of the different aspects may be mixed and matchedas desired to form new aspects, whether or not the new aspects areexpressly disclosed.

1. A glass comprising a plurality of components, the glass having acomposition of the components comprising: greater than or equal to 10.0mol. % and less than or equal to 40.0 mol. % P₂O₅, greater than or equalto 0.5 mol. % and less than or equal to 50.0 mol. % TiO₂, greater thanor equal to 0.5 mol. % and less than or equal to 35.0 mol. % K₂O,greater than or equal to 0.5 mol. % and less than or equal to 35.0 mol.% CaO, greater than or equal to 0.0 mol. % and less than or equal to50.0 mol. % Nb₂O₅, greater than or equal to 0.0 mol. % and less than orequal to 15.0 mol. % MgO, greater than or equal to 0.0 mol. % and lessthan or equal to 10.0 mol. % Al₂O₃, greater than or equal to 0.0 mol. %and less than or equal to 4.5 mol. % Li₂O, greater than or equal to 0.0mol. % and less than or equal to 1.0 mol. % V₂O₅, greater than or equalto 4.0 mol. % RO, greater than or equal to 0.0 mol. % and less than orequal to 20.0 mol. % for a sum of TeO₂+SnO₂+SnO, greater than or equalto 0.0 mol. % and less than or equal to 15.0 mol. % for a sum ofSiO₂+GeO₂and optionally comprising one or more components selected fromNa₂O, WO₃, BaO, SrO, ZnO, PbO, Bi₂O₃, B₂O₃, ZrO₂, Tl₂O, Ag₂O, Cs₂O,Ga₂O₃, La₂O₃, MoO₃ and Ta₂O₅, wherein the glass satisfies the condition:P _(n)−(1.54+0.1*P _(d))>0.00, where P_(n) is a refractive indexparameter calculated from the glass composition in terms of mol. % ofthe components according to the Formula (I):P_(n)=−0.0043794*P₂O₅+0.0072428*Nb₂O₅+0.0037304*TiO₂−0.00039553*BaO−0.0032012*K₂O−0.00060689*CaO−0.0024218*Na₂O−0.0014988*Li₂O+0.0028587*WO₃+0.0083295*Bi₂O₃−0.0031637*B₂O₃−0.0030702*SiO₂−0.00030248*ZnO+0.0020025*ZrO₂−0.0018173*MgO−0.0032886*Al₂O₃+0.0024221*TeO₂+0.0038137*PbO−0.0016392*GeO₂+0.0063024*Tl₂O+0.0048765*Ag₂O+1.81451,  (I)P_(d) is a density parameter calculated from the glass composition interms of mol. % of the components according to the Formula (II):P_(d)[g/cm³]=3.98457−0.015773*Al₂O₃−0.014501*B₂O₃+0.019328*BaO+0.060758*Bi₂O₃−0.0012685*CaO+0.023111*CdO+0.0053184*Cs₂O+0.011488*Ga₂O₃−0.0015416*GeO₂−0.013342*K₂O+0.058319*La₂O₃−0.007918*Li₂O−0.0021423*MgO−0.0024413*MoO₃−0.0082226*Na₂O+0.0084961*Nb₂O₅−0.020501*P₂O₅+0.038898*PbO−0.012720*SiO₂+0.013948*SrO+0.047924*Ta₂O₅+0.011248*TeO₂−0.0092491*V₂O₅+0.028913*WO₃+0.0074702*ZnO+0.0096721*ZrO₂,  (II)where RO is a total sum of divalent metal oxides, and a symbol “*” meansmultiplication.
 2. The glass of claim 1, wherein the glass satisfies thecondition:P _(n)−(1.58+0.1*P _(d))>0.00.
 3. The glass of claim 1, wherein theglass satisfies the condition:P _(d)<4.2 g/cm³.
 4. The glass of claim 1, wherein the glass satisfiesthe condition:P_(n)>1.8.
 5. The glass of claim 1, wherein the glass satisfies thecondition:P _(ref)>0.24 cm³/g, where P_(ref) is a refraction parameter calculatedfrom the glass composition in terms of mol. % of the componentsaccording to the Formula (IV):P_(ref)[cm³/g]=0.223637+0.0010703*Nb₂O₅−0.00041688*P₂O₅+0.00088482*TiO₂+0.000054956*CaO−0.00029243*K₂O−0.0008347*BaO−0.00023739*Na₂O+0.000082792*Li₂O−0.0012487*WO₃−0.00042393*ZnO−0.00059152*SrO−0.00018266*MgO−0.0014091*Bi₂O₃−0.0014895*Ta₂O₅−0.00021842*SiO₂−0.00024788*ZrO₂−0.00014801*B₂O₃−0.000060848*TeO₂−0.00085564*PbO−0.00042429*GeO₂−0.0015439*Tl₂O−0.0012936*Ag₂O−0.00089356*Cu₂O−0.00039278*CuO+0.00017895*As₂O₃−0.00011802*Sb₂O₃.  (IV)6. The glass of claim 1, wherein the composition of the componentscomprises: greater than or equal to 15.0 mol. % and less than or equalto 35.0 mol. % P₂O₅, greater than or equal to 10.0 mol. % and less thanor equal to 40.0 mol. % Nb₂O₅, greater than or equal to 0.5 mol. % andless than or equal to 40.0 mol. % TiO₂, greater than or equal to 0.5mol. % and less than or equal to 30.0 mol. % CaO, greater than or equalto 0.5 mol. % and less than or equal to 20.0 mol. % K₂O, greater than orequal to 0.0 mol. % and less than or equal to 20.0 mol. % BaO, greaterthan or equal to 0.0 mol. % and less than or equal to 20.0 mol. % Na₂O,greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol.% WO₃, greater than or equal to 0.0 mol. % and less than or equal to 4.0mol. % Bi₂O₃ and greater than or equal to 0.0 mol. % and less than orequal to 2.0 mol. % Ta₂O₅.
 7. The glass of claim 1, where thecomposition of the components comprises: greater than or equal to 21.0mol. % and less than or equal to 30.0 mol. % P₂O₅, greater than or equalto 13.0 mol. % and less than or equal to 38.0 mol. % Nb₂O₅, greater thanor equal to 9.0 mol. % and less than or equal to 37.0 mol. % TiO₂,greater than or equal to 4.0 mol. % and less than or equal to 23.0 mol.% CaO, greater than or equal to 4.0 mol. % and less than or equal to16.0 mol. % K₂O, greater than or equal to 0.0 mol. % and less than orequal to 14.5 mol. % BaO, greater than or equal to 0.0 mol. % and lessthan or equal to 13.5 mol. % Na₂O, greater than or equal to 0.0 mol. %and less than or equal to 8.5 mol. % WO₃, greater than or equal to 0.0mol. % and less than or equal to 3.4 mol. % Bi₂O₃, greater than or equalto 0.0 mol. % and less than or equal to 1.8 mol. % Ta₂O₅ and greaterthan or equal to 0.0 mol. % and less than or equal to 0.9 mol. % SiO₂.8. The glass of claim 1, wherein the composition of the componentscomprises: greater than or equal to 22.0 mol. % and less than or equalto 29.0 mol. % P₂O₅, greater than or equal to 16.0 mol. % and less thanor equal to 35.0 mol. % Nb₂O₅, greater than or equal to 12.0 mol. % andless than or equal to 34.0 mol. % TiO₂, greater than or equal to 5.5mol. % and less than or equal to 20.5 mol. % CaO, greater than or equalto 5.0 mol. % and less than or equal to 14.5 mol. % K₂O, greater than orequal to 0.0 mol. % and less than or equal to 13.0 mol. % BaO, greaterthan or equal to 0.0 mol. % and less than or equal to 12.0 mol. % Na₂O,greater than or equal to 0.0 mol. % and less than or equal to 7.5 mol. %WO₃, greater than or equal to 0.0 mol. % and less than or equal to 4.0mol. % Li₂O, greater than or equal to 0.0 mol. % and less than or equalto 3.0 mol. % Bi₂O₃, greater than or equal to 0.0 mol. % and less thanor equal to 1.6 mol. % Ta₂O₅ and greater than or equal to 0.0 mol. % andless than or equal to 0.8 mol. % SiO₂.
 9. The glass of claim 1, whereinwhen cooled in air from 1100° C. to 500° C. in 2.5 minutes, the glassdoes not crystallize.
 10. A glass comprising a plurality of components,the glass having a composition of the components comprising: greaterthan or equal to 10.0 mol. % and less than or equal to 40.0 mol. % P₂O₅,greater than or equal to 1.0 mol. % and less than or equal to 50.0 mol.% TiO₂, greater than or equal to 1.0 mol. % and less than or equal to35.0 mol. % K₂O, greater than or equal to 1.0 mol. % and less than orequal to 35.0 mol. % CaO, greater than or equal to 0.0 mol. % and lessthan or equal to 50.0 mol. % Nb₂O₅, greater than or equal to 0.0 mol. %and less than or equal to 15.0 mol. % MgO, greater than or equal to 0.0mol. % and less than or equal to 10.0 mol. % Al₂O₃, greater than orequal to 0.0 mol. % and less than or equal to 1.0 mol. % V₂O₅, greaterthan or equal to 4.0 mol. % RO, greater than or equal to 0.0 mol. % andless than or equal to 20.0 mol. % for a sum of TeO₂+SnO₂+SnO, greaterthan or equal to 0.0 mol. % and less than or equal to 15.0 mol. % for asum of SiO₂+GeO₂ and optionally comprising one or more componentsselected from Na₂O, Li₂O, WO₃, BaO, SrO, ZnO, PbO, Bi₂O₃, B₂O₃, ZrO₂,Tl₂O, Ag₂O, Ga₂O₃, MoO₃ and Ta₂O₅, wherein the glass satisfies theconditions:P_(n)>1.75 andP _(ν)−(64.5−23.4*P _(n))<0.00, where P_(n) is a refractive indexparameter calculated from the glass composition in terms of mol. % ofthe components according to the Formula (I):P_(n)=−0.0043794*P₂O₅+0.0072428*Nb₂O₅+0.0037304*TiO₂−0.00039553*BaO−0.0032012*K₂O−0.00060689*CaO−0.0024218*Na₂O−0.0014988*Li₂O+0.0028587*WO₃+0.0083295*Bi₂O₃−0.0031637*B₂O₃−0.0030702*SiO₂−0.00030248*ZnO+0.0020025*ZrO₂−0.0018173*MgO−0.0032886*Al₂O₃+0.0024221*TeO₂+0.0038137*PbO−0.0016392*GeO₂+0.0063024*Tl₂O+0.0048765*Ag₂O+1.81451,  (I)P_(ν) is a dispersion parameter calculated from the glass composition interms of mol. % of the components according to the Formula (III):P _(ν)=exp(2.11+0.0438*(exp(3.25980+0.0072248*Al₂O₃+0.0055494*B₂O₃+0.0024164*BaO−0.00849*Bi₂O₃+0.0029812*CaO+0.0092768*CdO+0.0099821*Ga₂O₃−0.0038579*GeO₂+0.0028062*K₂O+0.0031951*Li₂O+0.0027011*MgO+0.007976*MoO₃+0.0028705*Na₂O−0.013374*Nb₂O₅+0.0072007*P₂O₅−0.0049796*PbO+0.0032241*SiO₂+0.0050024*SrO−0.002136*Ta₂O₅−0.0032329*TeO₂−0.009788*TiO₂+0.0074782*V₂O₅−0.0057095*WO₃+0.0032826*ZnO+0.009302*ZrO₂))),  (III)where RO is a total sum of divalent metal oxides, and a symbol “*” meansmultiplication.
 11. The glass of claim 10, wherein the glass has arefractive index at 587.56 nm, n_(d), greater than or equal to 1.75, andwherein the glass satisfies the condition:ν_(d)−(63.7−23.4*n _(d))<0.00, where ν_(d) is an Abbe number of theglass.
 12. The glass of any claim 10, wherein the glass satisfies thecondition:ν_(d)−(63.7−23.4*n _(d))<0.00, where ν_(d) is an Abbe number of theglass, and n_(d) is a refractive index of the glass at 587.56 nm. 13.The glass of claim 10, wherein the glass satisfies the condition:P _(ν)−(63.7−23.4*P _(n))<0.00.
 14. The glass of claim 10, wherein theglass satisfies the condition:P _(d)<4.2 g/cm³, where P_(d) is a density parameter calculated from theglass composition in terms of mol. % of the components according to theFormula (II):P_(d)[g/cm³]=3.98457−0.015773*Al₂O₃−0.014501*B₂O₃+0.019328*BaO+0.060758*Bi₂O₃−0.0012685*CaO+0.023111*CdO+0.0053184*Cs₂O+0.011488*Ga₂O₃−0.0015416*GeO₂−0.013342*K₂O+0.058319*La₂O₃−0.007918*Li₂O−0.0021423*MgO−0.0024413*MoO₃−0.0082226*Na₂O+0.0084961*Nb₂O₅−0.020501*P₂O₅+0.038898*PbO−0.012720*SiO₂+0.013948*SrO+0.047924*Ta₂O₅+0.011248*TeO₂−0.0092491*V₂O₅+0.028913*WO₃+0.0074702*ZnO+0.0096721*ZrO₂.  (II)15. The glass of claim 10, wherein the glass satisfies the condition:P_(n)>1.8.
 16. The glass of claim 10, wherein the glass satisfies thecondition:P _(ref)>0.24 cm³/g, where P_(ref) is a refraction parameter calculatedfrom the glass composition in terms of mol. % of the componentsaccording to the Formula (IV):P_(ref)[cm³/g]=0.223637+0.0010703*Nb₂O₅−0.00041688*P₂O₅+0.00088482*TiO₂+0.000054956*CaO−0.00029243*K₂O−0.0008347*BaO−0.00023739*Na₂O+0.000082792*Li₂O−0.0012487*WO₃−0.00042393*ZnO−0.00059152*SrO−0.00018266*MgO−0.0014091*Bi₂O₃−0.0014895*Ta₂O₅−0.00021842*SiO₂−0.00024788*ZrO₂−0.00014801*B₂O₃−0.000060848*TeO₂−0.00085564*PbO−0.00042429*GeO₂−0.0015439*Tl₂O−0.0012936*Ag₂O−0.00089356*Cu₂O−0.00039278*CuO+0.00017895*As₂O₃−0.00011802*Sb₂O₃.  (IV)17. The glass of claim 10, wherein the composition of the componentscomprises: greater than or equal to 15.0 mol. % and less than or equalto 35.0 mol. % P₂O₅, greater than or equal to 10.0 mol. % and less thanor equal to 40.0 mol. % Nb₂O₅, greater than or equal to 1.0 mol. % andless than or equal to 40.0 mol. % TiO₂, greater than or equal to 1.0mol. % and less than or equal to 30.0 mol. % CaO, greater than or equalto 1.0 mol. % and less than or equal to 20.0 mol. % K₂O, greater than orequal to 0.0 mol. % and less than or equal to 20.0 mol. % BaO, greaterthan or equal to 0.0 mol. % and less than or equal to 20.0 mol. % Na₂O,greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol.% WO₃, greater than or equal to 0.0 mol. % and less than or equal to 5.0mol. % Li₂O, greater than or equal to 0.0 mol. % and less than or equalto 4.0 mol. % Bi₂O₃ and greater than or equal to 0.0 mol. % and lessthan or equal to 2.0 mol. % Ta₂O₅.
 18. The glass of claim 10, whereinthe composition of the components comprises: greater than or equal to21.0 mol. % and less than or equal to 30.0 mol. % P₂O₅, greater than orequal to 13.0 mol. % and less than or equal to 38.0 mol. % Nb₂O₅,greater than or equal to 9.0 mol. % and less than or equal to 37.0 mol.% TiO₂, greater than or equal to 4.0 mol. % and less than or equal to23.0 mol. % CaO, greater than or equal to 4.0 mol. % and less than orequal to 16.0 mol. % K₂O, greater than or equal to 0.0 mol. % and lessthan or equal to 14.5 mol. % BaO, greater than or equal to 0.0 mol. %and less than or equal to 13.5 mol. % Na₂O, greater than or equal to 0.0mol. % and less than or equal to 8.5 mol. % WO₃, greater than or equalto 0.0 mol. % and less than or equal to 4.5 mol. % Li₂O, greater than orequal to 0.0 mol. % and less than or equal to 3.4 mol. % Bi₂O₃, greaterthan or equal to 0.0 mol. % and less than or equal to 1.8 mol. % Ta₂O₅and greater than or equal to 0.0 mol. % and less than or equal to 0.9mol. % SiO₂.
 19. The glass of claim 10, wherein the composition of thecomponents comprises: greater than or equal to 0.0 mol. % and less thanor equal to 4.5 mol. % Li₂O.
 20. The glass of claim 10, wherein whencooled in air from 1100° C. to 500° C. in 2.5 minutes, the glass doesnot crystallize.